Touch at a Distance: Underwater Object
Identification Using Pressure Sensors
by
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JUL 2 9 2011
Audrey Maertens
LIBR
Ingenieure de l'Ecole Polytechnique (2009)
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
ARCHWES
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2011
@
Massachusetts Institute of Technology 2011. All rights reserved.
A uthor ................
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ical Engineering
May 6, 2011
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Michael S Triantafyllou
Professor of Mechanical and Ocean Engineering
Thesis
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David Hardt, Professor of Mechanical Engineering
Chairman, Department Committee on Graduate Theses
Touch at a Distance: Underwater Object Identification Using
Pressure Sensors
by
Audrey Maertens
Submitted to the Department of Mechanical Engineering
on May 6, 2011, in partial fulfillment of the
requirements for the degree of
Master of Science in Mechanical Engineering
Abstract
While the vast majority of underwater vehicles rely exclusively on sonar and vision
to detect obstacles and maneuver, live fish also use their lateral line organ. The role
played by the canal lateral line system is particularly important for hypogean fish,
such as blind Mexican cave fish, who use it to avoid obstacles and navigate dexterously
in complex environments. Similarly, pressure sensors could be used on underwater
vehicles to expand their range of operability by filling the gap left by sonar and vision
systems in turbid cluttered environments.
To understand how much information can be extracted from the artificial lateral
line of an underwater vehicle exploring an unknown environment, the case of a foil
passing a static object in still water is analyzed. A two-dimensional potential flow
approach based on a source panels method is used to characterize the spatio-temporal
pressure signature of the object as sensed by the vehicle. Simulations are used to
estimate the sensing range of an artificial lateral line and the appropriate density of
pressure sensors.
To emulate the object-detection and shape-recognition capabilities of the lateral
line, an adapted unscented Kalman filter is combined with the hydrodynamic model.
The method developed is experimentally tested in a water tank, using a hydrofoil
instrumented with pressure sensors passing a static cylinder. The results show that
location and shape informations of an elliptical cylinder can be successfully inferred
from experimental pressure measurements. Performance of the proposed method for
object identification using pressure sensors are discussed and ways to improve it are
suggested.
Thesis Supervisor: Michael S Triantafyllou
Title: Professor of Mechanical and Ocean Engineering
Acknowledgments
First of all, I would like to acknowledge my boyfriend and life partner, Fabien, for his
support and for dutifully proofreading this thesis.
I would like to acknowledge my advisor Prof. Michael Triantafyllou, as well as
Jason Dahl for their support and insight on this project.
In addition, I wish to thank Jeff Dusek for letting me use his experimental setup
and Vicente Fernandez who initiated this project. I would also like to acknowledge
the Singapore-MIT Alliance for Research and Technology for funding this research.
Finally, I would like to acknowledge my colleagues and friends for their occasional help and everyday support: Heather Beem, Dave Rival, James Schulmeister,
Stephanie Steele, Gabriel Weymouth.
Contents
17
1 Introduction
1.1
Research motivation
. . . . . . . . . . . . . . . . . . .
.
.
.
17
1.2
Biological inspiration: the lateral line . . . . . . . . . .
.
.
.
18
1.3
1.4
2
3
1.2.1
Morphology and physiology of the lateral line
.
.
.
18
1.2.2
Importance of the lateral line for hypogean fish
.
.
.
21
Previous work . . . . . . . . . . . . . . . . . . . . . . .
.
.
.
22
1.3.1
Hydrodynamics of lateral line stimuli . . . . . .
.
.
.
22
1.3.2
Bio-mimetic lateral lines . . . . . . . . . . . . .
.
.
.
24
Chapter preview
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
27
Object identification: theory
2.1
Discussion of existing methods . . . . . . . . . . . . . . . . . . . . . .
27
2.2
Shape characterization . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.3
The forward problem: hydrodynamic modeling . . . . . . . . . . . . .
30
2.4
The inverse problem
. . . . . . . . . . . . . . . . . . . . . . . . . . .
34
2.4.1
Choice of the inversion algorithm . . . . . . . . . . . . . . . .
34
2.4.2
The unscented Kalman filter . . . . . . . . . . . . . . . . . . .
35
Theoretical pressure distribution on a foil passing an object
3.1
39
Comparison between different scenarios . . . . . . . . .
39
3.1.1
Passive sensing . . . . . . . . . . . . . . . . . .
40
3.1.2
Active sensing . . . . . . . . . . . . . . . . . . .
41
3.1.3
Active sensing with external flow
. . . . . . . .
42
3.2
3.3
3.4
4
3.2.1
Variation in size and distance of a circular obstacle
. . . . . .
43
3.2.2
Elliptical shapes . . . . . . . . . . . . . . . . . . . . . . . . . .
47
3.2.3
More general shape variations . . . . . . . . . . . . . . . . . .
49
Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
3.3.1
Variation in distance of a circular obstacle . . . . . . . . . . .
52
3.3.2
Variation in size of a circular obstacle . . . . . . . . . . . . . .
54
3.3.3
Variation in eccentricity of an elliptical obstacle . . . . . . . .
54
3.3.4
Variation in orientation of an elliptical obstacle
. . . . . . . .
55
3.3.5
More elaborate shape variations . . . . . . . . . . . . . . . . .
56
Guidelines for the use of pressure sensors for active object identification 56
3.4.1
Sensing range . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
3.4.2
Sensor density . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
Experimental object identification
61
4.1
61
4.2
4.3
5
Characterization of the pressure distribution on a foil passing a cylinder 43
Experim ental set-up
. . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1
Instrumented hydrofoil and testing tank
. . . . . . . . . . . .
61
4.1.2
Flow visualization . . . . . . . . . . . . . . . . . . . . . . . . .
61
4.1.3
Experimental parameters . . . . . . . . . . . . . . . . . . . . .
62
Pressure measurements analysis . . . . . . . . . . . . . . . . . . . . .
63
4.2.1
Noise characteristics
64
4.2.2
Comparison between measured and simulated pressure
. . . . . . . . . . . . . . . . . . . . . . .
. . . .
65
Object identification using pressure measurements . . . . . . . . . . .
66
4.3.1
Process noise . .... . . . . . . . . . . . . . . . . . . . . . . .
66
4.3.2
Strategy and initialization . . . . . . . . . . . . . . . . . . . .
67
4.3.3
An example of object identification . . . . . . . . . . . . . . .
68
4.3.4
Performance of experimental object detection and identification
69
Discussion and further simulations
73
5.1
Sensing range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
5.2
Impact of sensor density on object identification . . . . . . . . . . . .
77
6
. . . . . . . . . . . . .
5.3
Pressure sensors or pressure gradient sensors?
5.4
Limits of the potential flow model . . . . . . . . . . . . . . . . . . . .
Conclusions
7 Recommendations for future work
89
A Alternative definition of sensitivity
B Measurement-covariance matrices
C Pressure measurements figures
D Experimental object identification figures
101
10
List of Figures
1-1
The structure of superficial and canal neuromasts . . . . . . . . . . .
19
1-2
Schematic of the lateral line trunk canal
. . . . . . . . . . . . . . . .
20
2-1
Examples of shape estimation using a multipole expansion
. . . . . .
29
2-2
Boundary-value problem . . . . . . . . . . . . . . . . . . . . . . . . .
31
2-3
Surface discretization . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
3-1
Position along the foil
. . . . . . . . . . . . . . . . . . . . . . . . . .
39
3-2
Sketch of the problem and variables . . . . . . . . . . . . . . . . . . .
40
3-3
Passive pressure signature . . . . . . . . . . . . . . . . . . . . . . . .
41
3-4
Active pressure signature . . . . . . . . . . . . . . . . . . . . . . . . .
42
3-5
Combined pressure signature minus steady state . . . . . . . . . . . .
43
3-6
Pressure signature: variation in size and distance
. . . . . . . . . . .
44
3-7
Pressure signature differences: variation in size and distance
. . . . .
44
3-8
Active pressure signature in more extreme cases . . . . . . . . . . . .
45
3-9
Pressure drop amplitude: variation in size and distance. . . . . . . . .
46
3-10 Pressure spread: variation in size and distance . . . . . . . . . . . . .
47
3-11 Cylinders used to investigate changes in horizontal and vertical radius
48
3-12 Pressure signature: variation in horizontal and vertical radii . . . . .
48
3-13 Pressure difference: variation in horizontal and vertical radii . . . . .
49
3-14 Pressure difference: variation in orientation . . . . . . . . . . . . . . .
50
3-15 Pressure difference: triangle and square shapes . . . . . . . . . . . . .
51
3-16 Pressure difference: comparison between cutting the top of an ellipse
and changing its aspect ratio.
. . . . . . . . . . . . . . . . . . . . . .
51
. . . . . . . . . . . . . . . . . . . . . . . . . .
53
. . . . . . . . . . . . . . . . . .
53
3-19 Sensitivity to size . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3-20 Sensitivity to eccentricity for a horizor tal ellipse . . . . . . . . . . . .
55
3-21 Sensitivity to orientation
.. ..... .. ... .. ... .
55
3-22 Sensitivity to shape . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
3-23 Pressure gradient signatures.....
... .... ... ... .. ...
59
3-17 Sensitivity to distance
3-18 Sensitivity to distance for fixed sizes
4-1
Experimental set-up
. . . . . . . . . ... .... ... ... .. ...
62
4-2
Flow visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
4-3
Pressure traces and power spectra..
64
4-4
Theoretical and measured pressure on a foil passing a cylinder. ....
65
4-5
Experimental object localization . . .
. . . .
68
4-6
Experimental object identification . .
. . . .
68
4-7
Measured, filtered and predicted pressure . . . . . . . . . . . . . . . .
69
5-1
Identification of an ellipse located at maximum sensing distance. . . .
5-2
Identification of an ellipse located at maximum sensing distance with
. . . . . . . . . . . . . . . . . .
outside flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-3
Identification of an ellipse located at maximum sensing distance, with
a drifting sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-4
Identification of an ellipse located at maximum sensing distance, with
a denser array of pressure sensors . . . . . . . . . . . . . . . . . . . .
5-5
Identification of an ellipse located at maximum sensing distance, with
a drifting sensor in a denser array of pressure sensors . . . . . . . . .
5-6
Identification of an ellipse located at maximum sensing distance, with
1/3 of the pressure sensors drifting
5-7 Convergence time and final error
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
5-8
Pressure gradient signature . . . . . . . . . . . . . . . . . . . . . . . .
5-9
Comparison between experimental and simulated velocity field . . . .
5-10 Flow separation: a pathline
. . . . . . . . . . . . . . . . . . . . . . .
5-11 Unsteady pressure gradient along thee foil
. . . . . . . . . . . . . . . . . . . . . . . . . .
91
. . . . . . . . . . . . . . . . . .
92
A-3 Sensitivity to size . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
A-4 Sensitivity to eccentricity for a horizontal ellipse . . . . . . . . . . . .
92
A-5 Sensitivity to orientation . . . . . . . . . . . . . . . . . . . . . . . . .
93
A-6 Sensitivity to shape . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
C-1 Pressure measurements, Run 1 . . . . . . . . . . . . . . . . . . . . . .
97
C-2 Pressure measurements, Run 2 . . . . . . . . . . . . . . . . . . . . . .
97
C-3 Pressure measurements, Run 3 . . . . . . . . . . . . . . . . . . . . . .
98
C-4 Pressure measurements, Run 4 . . . . . . . . . . . . . . . . . . . . . .
98
C-5 Pressure measurements, Run 5 . . . . . . . . . . . . . . . . . . . . . .
98
C-6 Pressure measurements, Run 6 . . . . . . . . . . . . . . . . . . . . . .
99
C-7 Pressure measurements, Run 7 . . . . . . . . . . . . . . . . . . . . . .
99
A-1 Sensitivity to distance
A-2 Sensitivity to distance for fixed sizes
D-i Object identification, Run 1 . . . . . . . . . ..
.. . . . . . . . . . .
102
D-2 Object identification, Run 2 . . . . . . . . . .
.. . . . . . . . . . .
103
D-3 Object identification, Run 3 . . . . . . . . . .
.. . . . . . . . . . .
104
D-4 Object identification, Run 4 . . . . . . . . . . . . . . . . . . . . . . . 105
D-5 Object identification, Run 5 . . . . . . . . . . . . . . . . . . . . . . . 106
D-6 Object identification, Run 6 . . . . . . . . . . . . . . . . . . . . . . . 107
D-7 Object identification, Run 7 . . . . . . . . . . . . . . . . . . . . . . .
108
14
List of Tables
4.1
Cylinder parameters.. . . . . . . . . .
. . . . . . . . . . . . . .
63
4.2
Results of experimental object identification . . . . . . . . . . . . . .
71
5.1
Object identification performance using simulated data . . . . . . . .
75
16
Chapter 1
Introduction
1.1
Research motivation
The aim of this project is to allow underwater vehicles to use spatially distributed
pressure sensors for mapping and navigation. Most underwater vehicles today rely
exclusively on sonar and vision to detect obstacles and maneuver. However, both
systems have limited capabilities and serious disadvantages, so the development of a
new sensing capability might expand the range of operability of underwater vehicles.
The main limitation of vision is that light does not propagate well in water. Natural light does not penetrate further than 100 to 200 meters below the surface, and
using vision at greater depths necessitates the use of powerful spotlights. However,
if the water is murky, even a powerful spotlight will be helpless at lighting up the
environment.
Sound usually propagates well in water, even though it can also suffer from scattering. However, sonars are very noisy: they strongly disturb the marine life ([30])
and are incompatible with any discretion requirement. Finally, sonars are not very
effective in cluttered or confined environments due to excessive sound reflection.
Evolution endowed fish with a lateral line, a simple passive system that allows
them to navigate dexterously, even in dark complex environments. Recent advancements in the area of microengineering will soon make it possible to build sensors that
match the size and mimic the functions and organization of the lateral line. While
underwater spotlights and sonars consume a lot of energy and are typically expansive
and cumbersome, artificial lateral lines could be a cheap alternative for a passive navigation system. However, the hydrodynamics involved needs to be better understood
in order to provide an efficient navigation system. It is the goal of this research to
gain insight into what the pressure distribution along a moving body can tell us about
the environment.
How far away can an object be detected? How much information on its shape can
be inferred from the measurements of an artificial lateral line? How should pressure
sensors be distributed? Here are a few questions that are addressed in this thesis.
1.2
1.2.1
Biological inspiration: the lateral line
Morphology and physiology of the lateral line
The mechanosensory lateral line is a hydrodynamic receptor system that allows all
fish and most amphibians to detect water motions around them. It is composed
of a collection of small mechanoreceptive units called neuromasts. Each neuromast
consists of a conglomeration of sensory hair cells associated with support cells that
secrete a gelatinous mass, the cupula. When water flows past the cupula, friction
causes it to move, which in turn deflects the cilia of the hair cells (Figure 1-iC). The
deflection of the cilia is then transduced into trains of action potentials which are
transmitted to the central nervous system for post-processing.
Fish possess hundreds to thousands of these neuromasts, located in various-but
stereotypical-positions on the head and trunk
([34]),
as illustrated in Figure 1-1A for
a blind Mexican cave fish (Astyanax mexicanus). There is evidence that the lateral
line is implicated in many behaviors such as schooling, courtship and spawning, prey
detection, predator avoidance, rheotaxis, and spacial orientation ([8], [5]).
In most fish, there are two lateral line submodalities: superficial neuromasts, isolated on the surface of the skin and scales, and canal neuromasts embedded in subdermal water-filled canals (Figure 1-1). Experiments that selectively disable either
Figure 1-1: The structure of superficial and canal neuromasts.
(A) Individual neuromasts appear as yellow points due to fluorescent staining [2-(4(dimethylamino)styryl)-N-ethylpyridinium iodide] of the hair cells in the blind Mexican cave fish (Astyanax mexicanus). (B) A magnified view of a portion of the head
highlights the different sizes of canal (solid circle) and superficial (dashed circle) neuromasts. (C) A schematic of a superficial neuromast illustrates its main anatomical
features. (D) A schematic drawing of a canal neuromast. Adapted from [35].
superficial or canal neuromasts suggest that the two subsystems respond to different
stimuli and play distinct roles in fish behavior ([27], [6], [21]). Superficial neuromasts
respond to the flow of water along the skin of the fish; they provide an important
source of information on currents in the environment of the fish and play a central role
in behaviors like rheotaxis ([27]). However, superficial neuromasts do not respond to
flow perturbations if the fish is exposed to running water ([11]).
The canals open to the environment at periodic intervals through pores, such that
there is usually one neuromast between two pores (Figure 1-2A). As a result, the
response of each canal neuromast to fluid motions inside the canal is proportional
to the pressure difference between the two surrounding canal pores as illustrated in
Figure 1-2B ([10], [7]). Unlike surface neuromasts, posterior canal neuromasts are
B
A
epidermis scale
pore
canal
P
neuromast
4
sensory
hair cel
sensory nerve
sensory
nerve
Figure 1-2: Schematics of a typical canal (A) and of the motion-sensing neuromast
between a pair of pores inside a canal (B). Adapted from [1].
not stimulated by running water, which allows them to detect flow perturbations in
any current condition ([111). Experiments by Jansen [21] and Coombs [6] also showed
that canal neuromasts respond to faster and smaller scale stimuli. Therefore, canal
neuromasts are important to behaviors that require information about fine spatial
details like prey localization and obstacle avoidance
([5]).
1.2.2
Importance of the lateral line for hypogean fish
The role played by the canal lateral line system is particularly important for hypogean
fish (that spend their life in deep caves), such as blind Mexican cave fish ([28]). In
the absence of light, hypogean fish cannot rely on vision to build up a 'picture' of
their environment: they use hydrodynamic imaging instead. Most hypogean fish have
a reduced visual system that they barely use, but an enhanced lateral line system.
Canal neuromasts seem to play an essential role in replacing vision as the major sense
by which blind cave fish perceive their surroundings. The flow-field that exists around
a gliding fish is perturbed by objects in its immediate vicinity and these perturbations are detected by the lateral line system. In this way fish can build up a 'picture'
of their environment, a process that has been called active 'hydrodynamic imaging'
([17]).
Behavioral experiments ([33],
[91)
showed that blind Mexican cave fish are not only
able to detect the presence of obstacles placed in their environment, but they are also
capable of encoding both their shape and size. Von Campenhausen [33] also showed
that fish trained to choose between doors of different shapes (horizontal and vertical
rectangles) would glide in front of the doors before making their choice. These experiments confirm the hypothesis that the lateral line, and more specifically the canal
subsystem, not only allows fish to navigate safely in unknown environments, but also
to build up a three-dimensional 'image' of their surroundings.
Pressure sensing is a primary sense for hypogean fish and a promising complementary sensory capability for underwater vehicles. Using micro-electromechanical
(MEMS) pressure sensors that would act like an artificial lateral line system has
the potential to enable underwater vehicles to navigate even when vision and sonars
cannot be used.
1.3
1.3.1
Previous work
Hydrodynamics of lateral line stimuli
The development of artificial lateral lines for underwater vehicles would enable imaging and navigation in environments where vision and acoustic sensing fail (such as
murky cluttered environments) with much less energy and more discretion than sonar,
since it is a passive system (as discussed in Section 1.1.1). But despite numerous articles published on the theme of fish lateral line system (see previous section), very
few studies have aimed at reproducing the ability of imaging of blind Mexican cave
fish into an artificial lateral line. So far, most of the work has been restricted to
localizing a prey modeled by a dipole ([15], [29], [5]), which is of limited usefulness
for underwater vehicles trying to navigate.
There are two essential aspects in object detection: the detection of objects themselves (mostly the effect on the flow of the no flux condition imposed at the object
surface), and the detection of their wake (if they are moving relative to the flow).
Since vortices are characterized by a very distinctive low pressure, pressure sensors are very efficient at tracking vortices. Experiments by Chagnaud [3] showed that
gold fish can detect a Karman vortex street and encode the vortex shedding frequency.
Franosch [13] developed a mathematical model to determine how vortex rings in a
Karman vortex street stimulate the canal lateral line of an axially symmetric body.
But objects in water do not only produce a wake, they also have their own hydrodynamic signature: they alter the flow surrounding them in way that depends on
their size and shape. As stated earlier, the vast majority of studies on the question of
object detection focused on the case of a vibrating or translating sphere ([29], [15]).
Despite our knowing that fish can encode shape
(133],
[9]), very little has been done
to understand the hydrodynamics involved in shape encoding. The first study aiming
at understanding the hydrodynamics of object identification was recently carried out
by Sichert [32]. Sichert laid the foundations of hydrodynamics mapping using velocity sensing. In his model, the shape of a moving body of revolution is described by
means of a multipole expansion and reconstructed-based on velocity readings by a
detecting body-using a maximum likelihood estimator. An important conclusion of
this work is that at a distance smaller than the moving object size, the velocity field
carries more information than its dipole simplification.
However, it has been shown experimentally that fish rely mainly on their canal
subsystem ([6]) to detect and identify obstacles. Based on this observation, Bouffanais
[2] investigated the forward and inverse problem of object detection and identification in outside flow using pressure sensing. He developed a parameterization that
separately encodes size, location and shape of a plane object and concluded that the
behavior of blind Mexican cave fish ([33])-'accelerate and glide past'-is probably
the most efficient one. Fish first get an estimate of the size and location of the obstacle, and then gather finer information on its shape.
Both studies ([32] and [2]) simplified the problem enough to make it possible to
use analytical models that help understanding the hydrodynamics involved. However,
neither of them took into account the disturbances caused by the sensing object itself.
In general, the pressure and velocity measured by the lateral line of a fish result from
interactions between the outside flow, the fish and the unknown object. In the most
extreme case-in the absence of outside flow-the only way for a fish to detect and
identify stationary obstacles is to generated flow itself. In this case, the lateral line
can be considered as an active sensing organ, and this is the behavior observed in fish
that glide past objects in still water tanks ([33]). However, in the case of a cruising
underwater vehicle trying to avoid obstacles, this active sensing does not require additional power input than what is necessary for cruising.
One of the only contributions to the understanding of the hydrodynamics involved
in active object detection is a 25 year-old study from Hassan ([16]). He modeled the
current around fish with a certain configuration of sources and sinks and used an
iterative method to ensure that no water fluxes through the body. He observed that,
when gliding past a circular cylinder, the spatio-temporal pressure signature along
the fish is unique for each combination of radius and distance. In the case of a frontal
approach, the results showed that the current velocity along the fish head increases
noticeably, but not until the fish is at a relatively short distance from the obstacle.
Slightly more recently, he used a method developed by Geer ([14]) to describe the flow
created by a slender body of revolution gliding toward or along a plane surface ([18],
[19]). This method models the alteration of the flow due to the presence of a slender
sensing body of revolution as a superposition of hydrodynamic poles continuously
distributed along the axis of the body.
No study has yet aimed at studying the hydrodynamics involved in active object
identification using the lateral line, and it is the goal of this thesis to lay the first
foundations for such studies.
1.3.2
Bio-mimetic lateral lines
In parallel to the recent development of hydrodynamic methods aimed at understanding stimuli of the lateral line, there has been a growing interest in trying to
manufacture artificial lateral lines. The development of both hydrodynamic tools
and sensing devices is crucial to be able to mimic the capabilities of blind Mexican
cave fish.
The main challenge in the design of artificial lateral lines is to fabricate sensors
that are small enough not to interfere with the flow while being sensitive enough to
detect flow structures. Fan [12] reported the first fabrication of an artificial lateral
line. He designed hair cell sensors (with a 820 pm tall cilium) that respond to flow
velocity in one direction. A few years later, Yang and Chen ([38], [4]) reported for
the first time the use of an artificial lateral line (consisting of 500 ptm high hot wire
anemometers) to detect both a dipole and the wake of a cylinder. Inspired by the
canal lateral line, they also proposed to package it as a canal to act like a high-pass
filter and avoid the signal to be overcome by strong DC components. This first example of use of an artificial lateral line to detect flow structures is very promising
and makes it more urgent to develop algorithms that will make it possible to use
this emerging sensing technology for underwater vehicle applications. More recently,
McConney [26] and Yang [39] reported designs of artificial lateral lines more closely
inspired from the fish lateral line with bio-mimetic neuromasts. Yang [39] also developed a beamforming algorithm (inspired from traditional sonar techniques) to localize
dipoles in three-dimensional space and successfully used it with his bio-mimetic lateral line to localize both a vibrating sphere and a tail-flicking crayfish. However, as
mentioned earlier, localizing vibrating spheres is of limited practical usefulness for
underwater vehicles.
No successful implementation of micromechanical pressure sensors to mimic the
the canal subsystem has yet been reported, but advancements in the area of microengineering that made the microfabrication of MEMS anemometers arrays possible
are likely to make the fabrication of MEMS pressure sensors possible in the next few
years.
1.4
Chapter preview
Chapter two introduces the problem studied in this thesis: a moving foil passing a
static object in stationary two-dimensional inviscid flow. It also presents the numerical approach used to solve it.
Chapter three describes the pressure distribution along the foil when passing an
object. Quantitative characterizations and guidelines for the use of pressure sensors
to identify object shapes are given.
Chapter four details experiments performed to test the proposed method. The
results of experimental object identification are also presented.
Chapter five discusses the performance of the object identification method proposed and several ways to improve it.
The limits of the inviscid model are also
discussed.
Chapter six draws conclusions on the research while recommendations for future
work on the project are proposed in Chapter seven.
26
Chapter 2
Object identification: theory
2.1
Discussion of existing methods
The simplest way to characterize the hydrodynamic signal measured by a natural
or artificial lateral line consists in modeling the problem in the context of twodimensional potential flow models. Comparisons between viscous and inviscid simulations of a dipole near a fish [29] showed similar pressure gradients in both cases.
They also showed important differences between the magnitude of the pressure gradient measured by a two-dimensional fish and a rotationally symmetrical one. However,
a two-dimensional study is always a good source of information as a preliminary study
before going for much more intensive three-dimensional simulations. We just need to
keep in mind that the results from two-dimensional studies cannot directly be generalized to three-dimensional cases.
Algorithms have recently been proposed to identify the shape of objects underwater using velocity
([31])
or pressure ([21) measurements. Both consider the case of
a moving object detected by the lateral line of a body that does not affect the flow.
The fact that the sensing body is considered as a 'ghost' might be a severe limitation,
especially when the two objects are close (and they have to be close enough for the
lateral line to sense information about the object shape). Interactions between the
two bodies are precisely what makes active sensing possible. Since the goal here is
to develop a model for active sensing, the possibility to extend either of these two
models to the case of several objects hydrodynamically interacting with each other
will now be briefly discussed.
Conformal mapping ([2]) is a very efficient and elegant way to map the potential
pressure field created by a moving object. It is also attractive because it gives a simple analytical expression of shapes. The conformal mapping study therefore provides
a good way to characterize the shape of an object and understand the role of each
parameter, especially the decreasing importance of shape parameters of increasing
complexity. However, it requires situation of interest to be the conformal map of a
configuration for which we know the analytical solution: there are very few of them.
A two-dimensional object in free space can be transformed into a circle through a
conformal map, and there is a known analytical solution for the pressure field around
a circle. But no conformal map could allow us to transform a configuration with two
objects into one for which a closed form solution is known. In conclusion, conformal
mapping is great to give understanding on simple configurations, but it is not flexible
enough to be adapted to more general cases.
The multipole expansion method ([31]) seems more flexible than the conformal
mapping while still giving a good insight into the decreasing importance of the multipole of increasing order. However, the spherical expansion used in [31] requires a
rotational symmetry that will usually be broken in the presence of two bodies. A
multipole expansion could still be used for a two-dimensional approach, which would
release the symmetry requirement. In this case, the velocity potential due to a stationary object in steady flow (of velocity U) can be written as ([25])
<D(+E)=
U - Y+
(
- )--.
(2.1)
n>1
This method has been tested in the simple case of a single object in a steady flow. The
pressure is measured along a circle around the object and the multipole expansion is
estimated using a standard least squares estimator. The shape is then estimated by
following the streamline corresponding to the stagnation point. Typical results are
shown in Figure 2-1. As can be seen from the top figures, the shape estimate can be
fairly accurate when the shape is not too different from that of a circle. However, the
bottom figures show that when the aspect ratio becomes significant (on the order of
2:1) the multipole approximation of the shape is very poor. The conclusion of these
tests is that the multiple expansion is good at approximating the far-field potential,
but not at estimating the shape of the object that created it.
Figure 2-1: Examples of shape estimation using a multipole expansion
As a conclusion, both analytical methods lack the flexibility needed to be extended
to more general problems like two objects hydrodynamically interacting. A flexible
'object based' (as opposed to 'far-field potential based') is needed. Since in potential
flow theory objects affect the flow through the no-flux condition imposed along their
surface, an intuitive way to represent them is a distributed flow source over their
surface ([25]).
Nonetheless, the conformal mapping method provides a convenient
shape characterization that can be used in this new framework.
2.2
Shape characterization
It is believed that blind cave fish can separately encode the distance, size and shape of
objects ([9]). Therefore, a convenient-and potentially biologically relevant-way to
parameterize the problem is to characterize an object by two parameters accounting
for its position, one size parameter and several shape parameters. Another desirable
feature of the parameterization is that the number of shape parameters needed to
account for the pressure decreases with the distance to the object. Bouffanais [2] proposed such a characterization. Taking inspiration from his work, we can characterize
objects by a parameterized curve:
S(O) = a + R
ei'+
p:Ake-ikO
00
(
,
G [0, 27r],
k=1
= x+iy+ R eZ +
|p
le0k(a -0)),
0 E
[0, 27r],
k=1
= xz
y +R
e
+ E(pkx
-+ ipky )e-ik
,
0 E [0, 27r]
(2.2)
k=1
where a (a = x + iy) refers to the location of the object 'center', R to its size and
each y4
(pk =
Ipk
leikok
= Pkx + ipky)
term is associated with a (k + 1)-gonal type of
perturbation of the shape from that of a circle. As k increases, the impact of the yk
term on the pressure field decays very quickly with distance from the cylinder ([2]).
For an ellipse of eccentricity e, only the first shape parameter p1 is non-zero:
|pil =
is a monotonous function of the eccentricity; a
= arg(pu1 ) is twice the
angle between the major axis and the horizontal axis; and R is the arithmetic mean
of the minor and major radii of the ellipse. Equivalently, the shape defined by the
parameterized curve S(O) = a + R pu("--O) is an ellipse of major radius R(1 +| p),
minor radius R(1- pl) and eccentricity
2
. It will also be useful later to notice that
the vertical radius of this ellipse (defined as the radius of the orthogonal projection
of the ellipse on the imaginary axis) is r, = R 1 - pl.
2.3
The forward problem: hydrodynamic modeling
The problem considered is the following: a moving 'fish-like' body (S( 1)) gliding at
constant speed (V) past a stationary object (S(0 ) in uniform flow (of velocity U).
Given the moving object, its trajectory, and the location (a), size (R) and shape (p)
of the stationary object, as well as the outside uniform stream, the velocity potential
anywhere in the flow field can be expressed in terms of a singularity distribution over
the surface of the objects
([20]).
The boundary-value problem considered is sketched
in Figure 2-2.
S 1)
V
Figure 2-2: Boundary-value problem
The velocity potential 4 may be decomposed as follows:
(() =
U . , + 0(s)
(2.3)
We are looking for the solutions of the following boundary-value problem:
In the fluid:
V2( = 0
-
Vp
=
0,
On SC0 :
On
1 ):
SM
At infinity:
(9n
o&n
V4D= U
=
(Z - U) -n,
(2.4)
-
The source formulation of the problem is:
X~)=
where S
JS
ofG~,)sf,
(2.5)
S(O)u(l), 6 is an unknown source distribution on the surface of the objects
and G(z, ()
=
-ln f - (| is the two-dimensional Rankine source Green function.
From Eq. 2.5, we have:
-.G
(2.6)
-(f (VI )ds(O).
an
Bn ('
Substituting Eq. 2.4 into 2.6, we obtain:
for 7 E S ()
U -
,G
an- (7, )ds(~
(2.7)
(V -- U) -
for 7E S ).
The approach used to numerically solve Eq. 2.7 for 6(e) consists in:
1. breaking up the surface S into N straight line segments,
2. assuming the source strength is constant over each line segment (panel).
The relation in Eq. 2.7 can then be evaluated by breaking up the integral as the sum
over all panels:
N
n (7, ()ds(()
a()
{
(V - U) - n
j=1 JSi
for 7
S().
(2.8)
for 7- SM.(
For I = sfi (f being the centroid position of the i-th panel) and 6j the source strength
of the j-th panel, Eq. 2.8 becomes:
N
j=1
S3 a
(6, ()ds(()0
( -K
if i E
(V - U) - i
if
I
(2.9)
E44 S)
6 is obtained by solving the linear system A6 = b. The velocity potential at any point
7 in the fluid can then be calculated by:
N
j=1
G(7, )ds()
Si
((2.10)
The velocity of the fluid can subsequently be computed using:
N
u=#
=U+E
1#G:,(ds()
(2.11)
S
j=1
Finally, the unsteady Bernoulli equation gives us:
p(i) =-P
()
+--I
(2.12)
+ C.
2
21
( 4t (
When the pressure is calculated on the surface S1, it is calculated as follows:
p
X)
V=
d(
dt ()V
p
P
=-p
--
dt)
di
dt
-
1
2
2
+ C
+ -|G|2
V
-
+ 2
+ C.
2
(2.13)
Since the pressure is calculated at the surface of the foil, it should always be estimated
at the center of a panel. In order to get a sense of the number of panels needed to
reasonably estimate the pressure measured along the foil, we consider the problem
sketched in Figure 2-3A, where the red dot on the foil represents the point where
the pressure is calculated. Each surface is broken up into segments of uniform size.
Figure 2-3B, shows the calculated pressure at the red dot when breaking up the foil
into 300 segments, and the circle into 10 to 200 segments. In Figure 2-3C, the circle
is broken up into 50 segments and the foil into 50 to 500 segments. With only 20
segments for the circle and 100 for the foil, the error falls below 5%. We can therefore
estimate that using 50 segments for the circle and 200 for the foil is a safe compromise
B
A
o
C
Circle discretization
0.08
0
0
0.06
-20
-20
0.04
-40
-40
0.02
-60
-10
-20
-80
-0
CL0.
0
W=.5 r/s
)p
Foil discretization
--
50
-100
-80
-200
(L
-200
0
-0.08 -0.06 -0.04 -0.02
Position(m)
0.02
0.04
0
0.05
0.1
0.15
0.2
Time(s)
-500
o10
-101
-0.02
0.25
0.3
Figure 2-3: Surface discretization
0
0.05
0.1
0.15
0.2
Time(s)
0.25
0.3
between accuracy and calculation time.
The combination of the shape parameterization presented in Section 2.2 and the
numerical potential flow model defines the forward methodology: relating pressure
measurements to the variables of interest (location, size, and shape).
2.4
The inverse problem
2.4.1
Choice of the inversion algorithm
Combined with an inversion technique, the forward model can be used to solve the
inverse problem: locating and identifying an object using pressure measurements. In
experiments, the pressure measured is corrupted by noise. For proper inversion, the
technique must be: 1) robust to noise, 2) capable of handling non-linearity, since the
pressure does not depend linearly on the characterizing parameters of the stationary
object and 3) dynamic, in order to be used in navigation of underwater vehicles.
A widely used class of algorithms to solve dynamical systems are Kalman filters.
Parameters can be efficiently estimated on-line by writing a state-space representation:
Xk+1
y
rk(2.14)
-
f (xk, uk)
1
e4
where x is the state vector (in our case, the shape we are trying to identify), r the
process noise, y the observation (in our case, the pressure measured by the lateral
line), e the measurement noise, u accounts for other parameters (location of the sensors, velocities) and
f is
the function that calculates the pressure at sensor locations
given a set of objects.
When
f
is not linear (as in our case), the most common approach is to use an
extended Kalman filter (EKF) which sirnply linearizes
f
so that the covariance and
mean of the state can be recursively estimated using a traditional linear Kalman Filter. But the assumption that a linearized transformation of means and covariances
is approximately equal to the true nonlinear transformation can be unsatisfactory for
highly nonlinear functions. And more important, the EKF requires the calculation of
the Jacobian of
f, for
which no analytical expression is available here.
Therefore, the unscented Kalman filter (UKF) [23] is probably more suitable to
solve this problem. Rather than approximating the function
f,
the UKF approxi-
mates the state probability density function by deterministic sampling. It is based on
two fundamental principles. First, it is easier to perform a nonlinear transformation
on individual samples than on a probability density function. Second, it is not too
hard to find a set of individual points in state space whose sample probability density
function (pdf) approximates the true pdf of a state vector. This set is found using the
unscented transformation in which 2n +I1 sigma points (n is the state dimension, here
the number of shape parameters) are chosen based on a square-root decomposition
of the prior state covariance. These sigma points (here they are object shapes) are
propagated through the true nonlinearity (the pressure function), without approximation, and a weighted mean and covariance is then calculated. This approach results
in approximations that are accurate to the third order (Taylor series expansion) for
Gaussian inputs for all nonlinearities. For non-Gaussian inputs, approximations are
accurate to at least the second-order [23].
The UKF is therefore more accurate than the more traditional EKF for highly
nonlinear problems. Moreover, it does not require the computation of derivatives for
which no analytical expressions are available here. It also samples the state pdf with
much less points than would be required by a Monte Carlo method, which makes it
better suited for real time applications.
2.4.2
The unscented Kalman filter
The unscented transformation
As introduced above, the unscented transformation chooses a set of 2n + 1 (sigma)
points so that their sample mean and covariance are x and P,,.
The nonlinear
function is applied to each point in turn to yield a cloud of transformed points; y and
Pyy are the statistics of the transformed points. We form a matrix X of 2n + 1 sigma
vectors Xi according to the following:
X0
-)
Xin
= + W(n + A)Pxx
Xi+n
=
In,
,Z i = 0, ...,
(2.15)
In,
(n + A)Pxx) , i = 0, ...,
(
where A = a 2 (n + r) - n is a scaling parameter. The constant a determines the
spread of the sigma points around R. It is usually set to a small positive value
(10-4 < a < 1) but the choice of the value will be discussed in the next section.
The constant r is a secondary scaling parameter, which is usually set to the heuristic
(
value 3 - n ([24]). Finally,
(n + A)Pxx) is the ith column of the lower-triangular
Cholesky factorization of (n + A) Pxx.
The sigma vectors are propagated through the nonlinear pressure function:
(2.16)
i = 0,. .. ,2n.
Yi =f (Xiu),
The mean and covariance for y are approximated using a weighted sample mean and
covariance of the transformed sigma points,
2n
Z
yi,
(2.17)
i=0
2n
W()(y
Py ~
-
y)(yi
(2.18)
-
i=0
with weights given by
n+A'
W(M)
where
#
WC)
-
WON = n+A _+
2(n-+ A)Z
1 - a2 +
,
(2.19)
(2.20)
is a parameter used to incorporate prior knowledge of the distribution of x
(for Gaussian distributions,
#
=
2 is optimal [23]).
Update equations
First, the shape and its covariance are initialized:
(2.21)
X0 = E[x],
P
=
O)(x -
E[(x -
0
2.22)
)T
In the absence of prior information, we initialize the shape to a circle and the covariance to a diagonal matrix, as will be discussed in Section 4.3. Then, at each time
step (each new pressure measurement), sigma vectors are calculated and the mean
and covariance of the shape are updated.
For k > 1, the time update (a priori values) and sigma vectors are calculated as
follows:
(2.23)
=X k-li
Xk
P-,
Xkik-1
=
x_
+ Rr_
[ lk
kC +
(2.24)
(n + A)P
:k -
(n + A)
,
(2.25)
(2.26)
Ykik_1 = f(Xkk _1, Uk),
2n
9k
S
=
(2.27)
W(m)yikk1
i=O
And the measurement update equations (optimal gain and updated shape and covariance) are:
2n
(Yikk1
PYy
-
Yk) (Yi,kk _1 -
1-
Xk)(Yi klk_1 -i
s k)T + Re,
(2.28)
i=0
2n
PXkYk =
(
W
(Xikk
)T,
(2.29)
i=0
gk
=
2.30)
P(P
k = ]-
PXk= Px
+ kk (Ykyk),
-
9k~~kg
(2.31)
(2.32)
where hats above letters stand for 'estimated value', R' is the process-noise covariance
and R' is the measurement-noise covariance.
Adapted unscented Kalman filter
The UKF described above is usually used assuming all distributions are Gaussian.
However, some configurations are not physical and cannot exist, this is the case of
two rigid bodies intersecting each other. Using non-physical configurations as our
sigma points can skew statistics and produce unusable results. One way to prevent
this from happening, is to properly tune the value of the parameters of the UKF.
This problem is avoided in two steps. We first ensure that, at each time step,
the a priori estimate of the object (iR) and the sensing body do not intersect. If
needed, the Kalman gain of the previous time step is scaled down to ensure the non
intersection.
Once the a priori configuration is valid, it is possible to find a radius r such that
all the configurations in the ball of center ik and radius r are valid. Therefore, the
parameter c-that determines the spread of the samples around the mean in the
unscented transform ([22])-can be chosen (for each time step) small enough that all
the sigma points are valid. a is set to its default value (a = 0.9) if it produces valid
sigma points.
The UKF and the forward model can now be combined to solve the inverse problem: locating and identifying an object in the flow using pressure measurements.
Chapter
Theoretical pressure distribution on a
foil passing an object
From now on, we will consider the case of a foil passing by an object.
The foil
considered in the rest of this thesis is a NACA 0018 foil (chord c = 15 cm, maximum
thickness T = 2.7 cm). The position along the foil is measured as the arc length
starting at the front, as shown in Figure 3-1. Only the pressure along the side of the
foil that is closest to the object will be considered.
Figure 3-1: Position along the foil (in)
3.1
Comparison between different scenarios
The lateral line can be used both as a passive or active sensing modality. In the
passive case, the fish relies on other bodies around it to interact with the flow and
create measurable flow patterns. In the active case, the fish itself creates the flow that
interacts with its environment. Flow perturbations due to the presence of objects are
measured by the lateral line and information about the environment is extracted. In
general, both mechanisms are at play simultaneously. To understand the differences
and interactions between the two mechanisms, three scenarios are considered: passive
sensing, active sensing, and the combination of both. In all the simulations presented,
the flow velocity (if non zero) is U = 0.1 m/s, the speed of the fish is V
=
0.5 m/s.
The object is a circular cylinder of radius r = 0.5T = 1.35 cm and the minimum
distance between the foil and the object is d
0.25T
6.75 mm. The problem
considered is sketched in Figure 3-2.
r
0
T
--V
Figure 3-2: Sketch of the problem and variables
3.1.1
Passive sensing
This is the case that has mainly been investigated so far ([2], [32]). In this scenario,
the foil measures pressure but is considered as a 'ghost' in that its effect on the flow is
ignored. This case is considered as a benchmark for the other scenarios. The pressure
along a 'ghost' foil as it passes the cylinder is plotted for three different angles of
outside flow in Figure 3-3.
The vertical axis represents the position along the foil (as defined in Figure 3-1).
The horizontal axis represents time as the foil passes the cylinder. The black dotted
line shows the orthogonal projection of the cylinder center on the foil.
Here, the pressure field is the well known superposition of a free stream and
a dipole. As the foil passes the cylinder, it simply measures this pressure field. In
=
A
E)=-3n/4
B
0i
8=-n/2
C
+30
20
-0.05
-0.05
-0.05
10
-0.15
0
-0.15
0
-0.15
0
-20
0
30
0.2
0.4
Time (s)
0.6
0.2
0.4
Time (s)
0.6
0.2
0.4
Time (s)
0.6
Figure 3-3: Passive pressure signature
the case considered, the foil measures a high or low pressure (depending on the flow
angle) of magnitude 30 Pa. The pressure signal measured by the foil simply gets
translated along the foil as it passes the cylinder. A horizontal or vertical slice of
the plots in Figure 3-3 would be enough to summarize the information they contain.
This means that measuring the pressure along the foil does not give significantly more
information than measuring the pressure at one point in time or at one location on
the foil.
3.1.2
Active sensing
In this case, the flow motion is generated by the foil. As can be seen in Figure
3-4A, the steady motion of the foil induces a high pressure at its front and a low
pressure along its side, which makes it hard to distinguish the pressure pattern due
to the presence of the object. Subtracting the steady state pressure reveals a pressure
pattern (Figure 3-4B) very different from the passive case one. This pattern is much
more complicated than in the passive case, so it potentially bears more information.
Unless explicitly mentioned, the pressure will always be plotted after subtraction of
the steady pressure.
The spatio-temporal pressure signature is characterized by a pressure peak at
the front followed by a drop along the thickest part of the foil. The last third of
the foil is only very weakly affected by the presence of the object. Contrary to the
passive sensing case, time and space give different information, and disposing of a
dense enough array of MEMS pressure sensors would experimentally make it possible
A
B Unsteady pressure
Total pressure
30
20
100
-0.05
50
-0050
10
0 (Pa) .0
-0.1
0
a-
a.-50
(Pa)
-0.1
-10
-20
-0.151-0
0
-30
-0.151
0.2
0.4
Time (s)
0.6
0
0.2
0.4
Time (s)
0.6
Figure 3-4: Active pressure signature
to take advantage of all the information. As the foil passes the object, the object
experiences various flow velocities and directions, hence giving richer information than
in the passive case. The spatio-temporal pressure characteristics will be investigated
in the second part of this chapter. On the downside, the pressure signal amplitude is
the same as in the passive case even though the speed of the foil is five times greater
than what the flow speed was. This is due to the fact that the flow velocity at the the
object decreases as the foil passes further away. For this reason, the pressure signal
will also decrease faster with distance in this case than in the passive one.
3.1.3
Active sensing with external flow
Self-generated and outside flow can be combined in order to take advantage of the two
scenarios described above. In this case, unlike in the passive case, the magnitude of
the pressure signal strongly depends on the orientation of the outside flow compared
to the motion of the foil. If the foil moves against the current (Figure 3-5A), the
effective velocity of the foil is greater, and the effects of both flows add up to create
a very strong pressure dip as the foil passes the object (of magnitude 200 Pa, as
compared to 30 Pa with the outside flow or self-generated flow alone). In the case
when the foil moves perpendicular to the outside current (Figure 3-5C), the pressure
signal much weaker, except at the very front of the foil as it approaches the cylinder.
An oblique current (Figure 3-5B) leads to an intermediate effect.
The simultaneous presence of outside and self-generated flows potentially allows to
take advantage of both. Due to the presence of the outside current, the flow velocity
e=-n
A
6=-3n/4
B
E)=-n/2
C
0
0
0
200
-0.05
-0.05
-0.05
100
-01
-0.1
0
-0.1
0.1
(Pa)
-100
-0.15
0
0.2
0.4
Time (s)
0.6
-0.15
0
0.2
0.4
Time (s)
0.6
-0.15 -0
-0.2
--
0.4
Time (s)
0.6
200
Figure 3-5: Combined pressure signature minus steady state
at the object does not drop as the foil gets further. Thanks to the self-generated
flow, the pressure distribution changes with time if the foil passes close enough to it.
Moreover, depending on the direction of the flow, both effects can add up to generate
a very strong pressure signal. In this perspective, active sensing in the absence of
external flow can be considered as a 'worst case scenario'. This is the case that we
will investigate in the next section.
3.2
Characterization of the pressure distribution on
a foil passing a cylinder
This section investigates the pressure distribution on a foil passing objects of various
sizes without external flow. Hassan [16] has already discussed the spatio-temporal
pressure distribution on a foil passing circular cylinders of various sizes and distances,
but the question has remained unaddressed since then. Here, we will first discuss
variations in size and distance for a circular cylinder, and extend the discussion to
ellipses and more complex shapes (like triangles).
3.2.1
Variation in size and distance of a circular obstacle
Figure 3-6 shows the pressure signature of circular cylinders of radius 0.3T and 0.5T
and at distance 0.2T and 0.3T. The general pattern of the spatio-temporal pressure
distribution is the same as described earlier, but for different cylinders, it differs in
peak (and drop) amplitude and spread. For a larger object (Figure 3-6B), the pressure
signal is stronger; as the object is moved away (Figure 3-6C), the pressure signal gets
weaker but its spread increases. As the object gets simultaneously further and smaller
(Figure 3-6C, by a factor 1.6), only the spread of the pressure signal is affected.
A
d=0.2T, r=0.3T
d=0.2T, r=1 .6*0.3T
40
20
-0.05
0 (Pa)
0
S-0.1
-0.1
-20
-0.15i
-0.15
0
B
02
0.4
Time (s)
0
0.6
0.2
0.4
Time (s)
0.6
-40
C d=1.6*0.2T, r=1.6*0.3T
d=1.6*0.2T, r=0.3T
n..
40
20
-0.05
0
(Pa)
0 -0.1
0.
-20
51 --.
0
ii llill, i
-0.15 1 -
.:
0.2
0.4
Time (s)
0.6
0.2
0
0.4
Time (s)
0.6
-40
Figure 3-6: Pressure signature: variation in size and distance
These observations are confirmed by Figure 3-7 where the pressure signature of
the reference cylinder (r = 0.2T, d = 0.3T) has been subtracted to the other pressure
signatures for easier comparison.
0
A
B
d=0.2T, r=1.6O.3T
C
d=1.6*0.2T, r=0.3T
d=1.6*0.2T, r=1.6*0.3T
15
)I-
10
-0.05
-u u:
5
-0.1
0
S-0.1
0 (Pa)
-0:-
-0.1
-5
-10
-0151
0
x
0.2
0.4
Time (s)
0.6
-0.15
-0.15l
0
0.2
0.4
Time (s)
0.6
0
0.2
0.4
Time (s)
0.6
-15
Figure 3-7: Pressure signature differences: variation in size and distance
Figure 3-8 shows pressure signals for more extreme cases: A) a very small and
very close object; B) an object ten times bigger and further; and C) a very big object.
The figure shows that the general pattern of the spatio-temporal pressure distribution
along the foil remains the same even in these more extreme configurations.
The
amplitude and spread of the pressure signal can vary by several orders of magnitude,
but here again, the amplitude of the pressure drop seems to be conserved when r/d
is constant.
A
B
d=O.1T, r=O.OST
0
C0
5
d=O.3T, r-ST
100
-0.06
-0.05;
0
-
-0. 15\
0.2
04
Time (s)
0.6
50
0
-0.1
0
0
5
-o.0 1
0-
C
d=Tr=0-ST
0
-0.15
(Pa)
0
0
0
0,2
-
--
04
Time (s)
-0.1
-50
5-. 5-0
0.6
(Pa)
0
0.2
0.4
Time (s)
0,6
(Pa)
Figure 3-8: Active pressure signature in more extreme cases
The previous observations suggest that the amplitude and spread of the pressure
signal are two relevant features to look at in order to determine the size and position
of a circular cylinder based on its pressure signature. To generalize and quantify
these observations, the amplitude of the pressure drop (max(-p)) has been plotted
in logarithmic scale (Figure 3-9A) as a function of distance (d) and radius (r) of the
cylinder, for d ranging from 0.1T to 10T and r from 0.05T to 5T. The pressure
can locally be approximated by a linear regression in logarithmic space. To classify
configurations in terms of distance and size of the object, Figure 3-9B shows linear
regressions for the four quadrants delineated by d
=
T and r
=
0.5T. The equation
of each plane is written in the corresponding quadrant.
It has been observed with Figures 3-6 and 3-7 that the pressure drop amplitude
seems to be a function of the ratio r/d. The linear regression (Figure 3-9B) shows
that for O.1T < d < T and 0.05T < r < 0.5T, it can indeed be approximated by
a function of r/d: max(-p)
-
10(r/d)
5
Pa. However, this is not the case for all
configurations:
* For bigger cylinders, the dependence on the size of the cylinder gets weaker: for
O.1T < d < T and 0.5T < r < 5T, max(-p) ~ 10(r/T)0 2 (T/d) Pa.
B
A 20*log(rnax(-p))
A0.5o~ax~)
.5
Linear regressions
Lna ersin
40
20
0
0
0
-20
-0.5
~-0.5
-1
-1
-40
-60
-0.5
0
log(d/T)
0.5
1
-0.5
0
log(d/T)
0.5
-80
1 (dB re iPa)
Figure 3-9: Pressure drop amplitude: variation in size and distance.
" For further cylinders, the dependence on the distance gets stronger: for T <
d < 10T and 0.05T < r < 0.5T, max(-p) ~ 30(r/T)2 (T/d)3 Pa.
* For further and bigger cylinders, both effects are combined, such that for T <
d < lOT and 0.5T < r < 5T, max(-p) ~ 10(r/T)(T/d)2.5 Pa.
It is interesting to notice that for small and close objects, the pressure amplitude
only depends on the ratio r/d, while for larger and further objects, it is roughly
proportional to the thickness of the foil. This is due to the fact that close to the
object, the flow velocity is dictated by that of the foil, while further away it also
depends on the amount of water displaced by the foil.
It has also been observed (Figure 3-6) that the pressure spread increases with
the distance of the object, but only gets weakly affected by its size. The pressure
spread is defined as the integral of the absolute value of the pressure over time and
over the length of the foil, normalized by the amplitude of the pressure drop (S =
f p/pz,,
dl dt). Figure 3-10A shows how the pressure spread changes with object
distance and size. Whereas the pressure drop amplitude decreases with distance and
increases with size of the cylinder, the spread (S) increases with both distance and
size. Figure 3-10B shows linear regressions for the same four quadrants as in Figure
3-9B.
e For small and far cylinders (T < d < lOT and 0.05T < r < 0.5T), the spread is
almost independent on the distance: S ~ 10-2(r/T)0 -6 m.s.
A 20*Iog(f~p/p
i dl dt)
B
0 .5
Linear regressions
-25
-30-30
0 .5
-35
-40
00
-. 5
-0.5
-45
-450
-1
-1
-50
-0.5
0
log(d/T)
0.5
1
-0.5
0
log(d/T)
0.5
-55
1 (dB re m 1s)
Figure 3-10: Pressure spread: variation in size and distance
* For bigger cylinders (T < d < lOT and 0.5T < r < 5T), the spread is slightly
more sensitive to changes in distance: S ~ 10-2(r/T)0 .5 (d/T)0 ' m.s.
" For closer cylinders (O.1T < d < T and 0.05T < r < 0.5T), the spread also is
slightly more sensitive to changes in distance: S ~ 10-2(r/T)0.7 (d/T)0
"
2
m.s.
For closer and bigger cylinders (0.01T < d < 0.1T and 0.OT < r < 5T), the
spread is almost as sensitive to distance as to size: S
10-2(r/T)05- (d/T)0
3
m.s.
3.2.2
Elliptical shapes
In this section we investigate (mainly qualitatively) how changes in aspect ratio and
orientation of a cylinder affect the spatio-temporal pressure distribution on the foil.
For a foil moving horizontally, we define the horizontal and vertical radii of an ellipse (respectively rh and r,) as shown in Figure 3-11. We define the radius (r) of
an elliptical cylinder as its mean radius: r
-
rlh"v
To understand how changes in
the three radii affect the pressure signature of the object, we compare in Figure 3-12
the pressure signature of a circular cylinder of radius r = 0.5T to elliptical cylinders
of eccentricity e = 0.75 with the same A) vertical radius; B) horizontal radius; and
C) radius, as sketched in Figure 3-11.
In the four cases plotted here, the minimum distance between the cylinder (as defined in Figure 3-2) is d = 0.32T. The general pattern of the spatio-temporal pressure
B
2rh
(DI2r
Figure 3-11: Cylinders used to investigate changes in horizontal and vertical radius
distribution is again the same for all cylinders, but slight differences in amplitude can
be observed. The most noticeable trend is that a larger horizontal radius produces a
much larger pressure signal.
r=O.5T,
A
=O
r=0.5T/(1-p), p=0.2
40
30
20
10
0 (Pa)
-10
-20
-30
-0.15
0
0.2
0.4
0
0.6
0.2
r=0.5T/(I+pA), p=0.
0.6
-40
Time (s)
Time (s)
B
0.4
2
C
0_
r=0.5T, pL=0.2
-0.05
0
0.2
0.4
Time (s)
0.6
0
0.2
0.4
0.6
Time (s)
Figure 3-12: Pressure signature: variation in horizontal and vertical radii
More information can be extracted from the pressure difference between the elliptical cylinders and the circular cylinder (Figure 3-13). Figure 3-13A shows that the
pressure peak and drop are both much stronger for a cylinder with a larger horizontal
radius. However, unlike Figure 3-7A (where both horizontal and vertical radii are
B
A r=-0.5T/(1-p), p=0.2
0__0
C
r=0O.5T/1+u), u=0.2
0
r=-0.5T, P=0.2
1
10
-0.05
EE
-0.05
-0.055
p"
O2
-0.1~
0 (Pa)
-0.10.
-01-5
-10
-. 5-0.15
0
0.2
04
Time (s)
-0. 15
0.6
0
0.2
04
Time (s)
0.6
0
-15
0.2
0.4
Time (s)
0.6
Figure 3-13: Pressure difference: variation in horizontal and vertical radii
larger), Figure 3-13A shows patterns slightly different from Figure 3-12: it is much
more symmetric as regards to the dashed line. Figure 3-13B shows that changing the
vertical radius has very little effect on the pressure signature of the cylinder. Figure
3-13C, that corresponds to an ellipse of intermediate size, exhibits an intermediate
pattern.
To visualize the effect of cylinder orientation on the pressure, Figure 3-14 shows
the pressure difference between a circular cylinder of radius r = 0.5T at distance
d = 0.32T and ellipses of same radius (located at the same distance) oriented at different angles. It can be observed that the pressure signal is stronger for the horizontal
ellipse (Figure 3-14A) and weaker for the vertical ellipse (Figure 3-14C), as explained
in the previous paragraph. For an ellipse oriented at r/4 (Figure 3-14B), the pressure
drops slightly earlier than for the cylinder due to the asymmetry of the configuration.
It is also interesting to notice that the pressure differences (when compared to a same
size circle) for ellipses of parameters yt and -- t are of opposite sign.
3.2.3
More general shape variations
Figure 3-15 shows the pressure difference between a circular cylinder of radius r
0.5T at distance d = 0.32T and almost triangular (Figures 3-15A and 3-15B) and
square shapes (Figures 3-15C and 3-15D). The corresponding shape is sketched in
the bottom left corner of each plot. As shapes become more elaborate, the pressure
signal also increases in complexity. However, the pressure difference (when compared
a=7/2
B
a=0
A
U
1'U
5
-0.05
-0.05
(Pa)
.20
-0.1
-0.1
-5
-0.15
-0-15
0
0
0.2
C
0.4
Time (s)
0.2
0
0.6
0.6
a=37/2
D
a=7
0.4
ime (s)
0
10
5
-0.05
-0.05
0
(Pa)
-0.15
-0.1
-10
0
0.2
0.4
Time (s)
0.6
0
0.2
0.4
Time (s)
0.6
Figure 3-14: Pressure difference: variation in orientation, r
=
0.5T and
[A
0.2e
to a same size circle) for shape parameters of opposite signs are still opposite.
It has been observed in Figure 3-13 that changing the horizontal diameter of an
ellipse affects the pressure signature much more than changing its vertical diameter.
This is intuitively due to the fact that changing the horizontal diameter strongly
changes the shape of the ellipse close to the foil, whereas changing the vertical diameter mainly changes the shape of the ellipse further from the foil. Further from
the foil, the effects of the no-flux condition are more diffuse, and the fluid velocity is
smaller, so the pressure on the foil is primarily affected by the shape of the cylinder
closest to it. To confirm this interpretation and somehow quantify it, we investigate
the impact on the pressure signature of two transformations: cutting 1/4 of an ellipse and changing its aspect ratio (Figure 3-16). Figure 3-16C shows three cylinder
shapes. The reference cylinder (cylinder o) has parameters r
y1 = -0.2.
=
3.81 cm = 1.4T and
The foil passes at distance d = 0.32T of all cylinders. Figure 3-16A is a
plot of the spatio-temporal pressure difference between cylinders a and o, where a is
the same cylinder as o, cut at 3/4 of its height. There is only a 3 Pa difference, despite
the fact that 1/4 of the ellipse has been cut. Cylinder b shows how much (or how
A
2/2
B
A
OL2=0
5
-0.05
E
0 (Pa)
-0.1
-0.1 51
-0.15
0
0.2
0.4
Time (s)
0.6
0
0
-5
0.6
0
5
-- 0.0
0-0
0.4
Time (s)
L3
=/3
D
a3=0
C
0.2
-0.05
1
0
-0.15
0
-0.1
-0.15
0.2
0.4
Time (s)
0.6
0
0.2
0.4
Time (s)
0.6
Figure 3-15: Pressure difference: triangle and square shapes. For A and B,
and p2 = 0.le 2ia2. For C and D, i = A 2 = 0 and 13 = 0.67e 3ia.
A p=-0.2, cut at 3/4 of height
B
p=-0.17
C
i
=0
Cylinder shapes
0P
-0.05
-0.05
0 (Pa)
Ob
-1
-2
-0.15
-0.15
0
0.2
0.4
Time (s)
0.6
0
0.2
0.4
Time (s)
Figure 3-16: Pressure difference: comparison between cutting the top of an ellipse
and changing its aspect ratio.
little) you need to alter the aspect ratio of ellipse o to get a pressure difference of the
same magnitude (as plotted in Figure 3-16B): you do not need to alter it much. The
pressure difference due to cutting the cylinder is more global because, as mentioned
earlier, changes in the shape far from the foil produce diffuse pressure differences, but
the amplitude is the same as when subtracting 0.03 from p.
3.3
Sensitivity analysis
We now have a good picture of the spatio-temporal pressure distribution on a foil
passing an object and how it is affected by changes in distance, size and shape of the
object. Since our goal is to locate and identify objects using pressure sensors, it is
of interest to know how sensitive the pressure measured by the foil is to variations
of these parameters. A quantitative sensitivity analysis is carried out in this section.
We define the pressure sensitivity in parameter x as Sx = max (|dp/dxl) because it is
easy to relate to technical limitations. Plots of sensitivity defined as the integral over
the length of the foil and over time of |dp/dx| can also be found in Appendix A.
3.3.1
Variation in distance of a circular obstacle
Figure 3-17 shows the pressure sensitivity to distance (d = d/T) and how it depends on the distance and size of the cylinder. In accordance with intuition, the
pressure is most sensitive to distance for close and big objects. A linear regression
in logarithmic space (Figure 3-17B) gives a rough approximation of the sensitivity
as Sg ~ 10(r/T)(T/d)3 . However, a closer look at Figure 3-17A reveals that the
sensitivity decreases fastest for far and small objects. Sensitivity to distance is plotted as a function of distance in Figure 3-18 for r = 0.05T, r = 0.5T and r = 5T.
Linear regressions for r = 0.5T are plotted for d < T and d > T. It shows that
a better approximation for the sensitivity is Sg ~ 20(r/T)(T/d)2 for d < T and
Sg ~ 40(r/T)(T/d)4 for d > T. This result indicates that sensitivity to distance
decreases very quickly when objects get further than the foil thickness.
A
20*log(max(|dp/ dd))
B
Liner regression
60
lx+23MX
40
20
0
-20
-0.5
-40
-60
-0.5
0
log(d/T)
0.5
1
-0.5
0
log(d/T)
0.5
1
Figure 3-17: Sensitivity to distance
log(d/T)
Figure 3-18: Sensitivity to distance for fixed sizes
-80
(dB re 1Pa)
3.3.2
Variation in size of a circular obstacle
Figure 3-19A shows the pressure sensitivity to size (r = r/T) and how it depends on
the distance and size of the cylinder. The sensitivity decreases with distance but is
not monotonic with size. For a given distance d, the sensitivity to size is maximum
for r/T
=
0.6N/d/T. The sensitivity to size is plotted against distance in Figure
3-19B for r = 0.05T, r = 0.5T and r = 5T. Linear regressions for r = 0.5T are
plotted for d < T and d > T and give the approximation S,
S , ~30(T/d) 3 for d > T. For r
=
-
20(T/d) for d < T and
0.05T, S, ~ 2(T/d) on the whole distance range
considered. For r = 5T, Sf,~ 3(T/d) 3 for d > 0.3T.
A
20*Iog(max(jdp/drl))
B
60
0.5
50
y=-21 x+25
40
20
y=--57x+29
0
0
0
-20
E
-0.5
-40
-
0
-60
-
-0.5
0
log(d/T)
0.5
-80
1 (dB re 1Pa)
-50
-1
r0.05T
r=0.5T
r=5T
-0.5
0
log(d/T)
0.5
1
Figure 3-19: Sensitivity to size
3.3.3
Variation in eccentricity of an elliptical obstacle
Figure 3-20A shows the pressure sensitivity to eccentricity for a horizontal ellipse of
radius r
=
0.5T and how it depends on the distance and eccentricity of the ellipse.
The sensitivity in eccentricity is mostly independent of the eccentricity while it clearly
decreases with distance. The sensitivity to eccentricity is plotted against distance in
Figure 3-20B for y = 0 and yt = 0.5. Linear regressions for t = 0 are plotted for d < T
and d > T. They give the approximation S,, ~ 7(T/d) for d < T and S,,
for d > T.
13(T/d) 3
A
20*Iog(max(jdp/djpj))5
0
0.950
0.8
B
o p=0
40
*
p=0.5
0.730
20
,
0.
0.510
x
a0y=-23x+17
0.5M
0.4
00
E
10
0.3
0.2
-20
-30
-40
0.1
-0.5
20-
*
0
log(d/T)
0.5
0-
-20
y=-60x+22
-40.
-1
1
(dB re 1Pa)
-0.5
0
log(d/T)
0.5
1
Figure 3-20: Sensitivity to eccentricity for a horizontal ellipse
3.3.4
Variation in orientation of an elliptical obstacle
Figure 3-21A shows the pressure sensitivity to orientation (d
parameterized by r = 0.5T and |p|
=
a/(27r)) for an ellipse
=
0.2. For small distances, the sensitivity has
a slight non monotonic dependence on a (it is highest for a = 1/3 and a
2/3),
=
while it clearly decreases with distance. The sensitivity to orientation is plotted as a
function of distance in Figure 3-21B for a = 0.77r and a = 7r. Linear regressions for
a = 7r are plotted for d < T and d > T. They give the approximation S,
5(T/d)"
for d < T and S. ~ 14(T/d) 3 for d > T.
A
20*Iog(max(jdp/daj))
6
B
50
0.9*
0.8
40
0.7
30*
20
2
10
0.6
(;;!-
00
'5
-10
0.2
-20
0.1
-30
-40
0
log(d/T)
0.5
a=u
a=0.7-
20
X
14
-y=-32x+
0.3
-0.5
0
*0*
0
1
(dB re 1 Pa)
0
;
0
y=-59x+23
-20
-40'
-1
-0.5
Figure 3-21: Sensitivity to orientation
0
0.5
dog(/Tr)
1
3.3.5
More elaborate shape variations
Shapes, as defined in Eq. 2.2, are parameterized by a series of pk terms. Based on
the pressure field generated by an object in steady flow ([2]), the sensitivity to Pk is
expected to decrease faster with distance for larger ks. Sensitivity to yUk is plotted in
Figure 3-22 for k E {1, 2, 3} for cylinders of radius r = 0.5T. Considering a circle
as the reference shape, p 1 corresponds to an elliptical deformation, P2 to a triangular
deformation and p 3 to a square deformation. Whereas for d < T the sensitivity is
almost the same for the three pkS, at d = 10T, S, 1 ~ 6S,
2
-
30S 1 . For d > T, the
sensitivity to highest order terms decreases fastest, which confirms our expectations.
60
---ellipse
trangle
--- square
40
20
S-
2
0.
X
I-20
-40
-60
-80
-1
-0.5
0
0.5
log(d/T)
1
1.5
Figure 3-22: Sensitivity to shape
3.4
Guidelines for the use of pressure sensors for active object identification
3.4.1
Sensing range
In Section 3.3, we have characterized the maximum pressure measured by a foil passing
an object as a function of the size and distance of the object. We have also identified
the pressure sensitivity to changes with size, distance and shape of the object. We can
now use these results to estimate the capabilities of a foil equipped with distributed
pressure sensors in terms of object detection and identification.
Depending on the pressure sensors characteristics and background noise, we can
define Apo as our pressure resolution. As defined earlier, f = r/T and d
d/T are
the normalized radius and distance of the object.
We have observed in Section 3.2.1 that the pressure amplitude is about
max(-p) ~ 10
Pa,
for
j<
1,
(3.1)
for > 1.
~ Pa,
max(-p) ~ 10 d5/2
Using the fact that the pressure is proportional to the square of the foil velocity (V)
(see Section 2.3), we see that the ability to detect an object by passing in front of it
with a foil equipped with pressure sensors requires:
Apo < 40V2
Pa,
if
< 1,
(3.2)
if > 1.
Apo < 40V2don Pa '
Using our sensitivity analysis, the same reasoning can be applied to translate the
pressure resolution into resolution in terms of size, position and shape of the cylinder.
We know from Section 3.3.1 that a distance change Ad causes pressure variations of
order
Ap ~ 80V 2 Ad-~ Pa,
if d< 1,
d2~
(3.3)
Ap ~ 120V2Ad ~ Pa,
if d > 1.
d4
Therefore, the error in distance estimation E = Ad/d based on pressure measurements will be on the order of
{Ea
E
Apo d
8 0 V2 f
fd<1,
Ba Apo 2 d
if d1> 1.
120V
(3.4)
We can similarly use the results from Section 3.3.2 to approximate the error in size
estimation E = Ai/
for an object of diameter comparable to the thickness of the
foil. In general this will provide a lower bound of the error.
E
Quatiyig te
hae
Po~d
80V 2 f
ErEf~ 120V2 -
ifd2< 1
(3.5)
ifd>1
if > 1.
Quantifying the shape estimate precision is more complicated as it depends on more
parameters.
For the sake of argument, we can use the result of Section 3.3.3 to
estimate the conditions under which we will be able to distinguish a horizontal ellipse
of shape parameter y and radius r = 0.5T from a circle:
Apo < 30V2 Pa,
if j< 1,
d
Apo < 50V2-- Pa,
if d> 1.
(3.6)
Let us now consider the canonical example that we have used so far: a foil moving
at speed V = 0.5 m/s past a circular cylinder of radius r
=
0.5T. We assume here
that our pressure resolution is Apo = 5 Pa. According to Eq. 3.2, we will be able
to detect the presence of an object if its distance to the foil is less than 0.8T. To
have a 10% precision on our estimates of distance and size, we need to pass less
than 0.2T away from it. Finally, if the object was an ellipse of parameters r = 0.5T
and y = 0.1, we would need to pass 0.1T away to tell that it is not a circle. It is
also interesting to notice that, although when the object is far the pressure is more
sensitive to elliptical shapes than to triangular or square shapes, at the distance at
which you would be able to identify an ellipse, the pressure is as sensitive to triangular
and square deformations as to elliptical deformations. However, in terms of shape
estimation, trying to identify too many parameters might worsen the overall estimate.
3.4.2
Sensor density
The above discussion is purely based on variations in pressure due to the presence
of objects in the flow. However, the quality of the estimate will also depend on the
spatial density of sensors and sampling rate, as well as on the inference algorithm
used.
It has been observed that in the active object identification scheme, the pressure
signal is not simply translated in time, but each point along the foil measures a
different pressure trace. Therefore, high sampling frequency and high spatial density
are not equivalent. The signal is characterized by a pressure peak at the front followed
by a pressure drop along the first two thirds of the body, whereas the pressure along
the last third of the foil is only weakly affected by the presence of a nearby object.
This observation indicates that, to actively identify objects, pressure sensors should
be distributed along the first two thirds of the foil.
We have observed in Section 3.2.1 that the size and distance of an object can be
identified by looking at the pressure spread and amplitude. However, the pressure
signal needs to be looked at in more details to be able to identify the shape of an
object. The typical magnitude of the pressure gradient, for the case considered, is 1
kPa.m-' (see Figure 3-23). If we consider that 5 Pa is the smallest pressure difference
that can be resolved, then a spacing of 5 mm gives a virtually infinite resolution.
A
B
Pressure gradient
Pressure gradient
0
4000
J
500
2000
-- 0.0550
-- 0.05
E
E
0
S-0.1
0.
0
0
13.
-0.1
-2000
-4000
-0.15
0
0.2
0.4
Time (s)
0.6
(Pa/m)
-500
-0.15
0
0.2
0.4
Time (s)
0.6
(Palm)
Figure 3-23: Pressure gradient signatures: (A) for a cylinder of r = 0.5T and distance
d = 0.3T and (B) is the difference with a cylinder 1.5 times bigger and further away.
A positive pressure gradient corresponds to an increase in pressure from the front of
the foil to its tail.
60
Chapter 4
Experimental object identification
4.1
4.1.1
Experimental set-up
Instrumented hydrofoil and testing tank
Experiments have been conducted in the SMART (Singapore-MIT Alliance for Research and Technology) Centre testing tank in Singapore to test the method developed to identify objects in the flow using pressure sensors. The tank has dimensions
3.6 x 1.2 x 1.2 meters. As shown in Figure 4-1A, the moving body used to generate
flow motions and sense pressure is a NACA 0018 foil (chord c = 15 cm and span
s = 60 cm) cast with internal 3.18 cm PVC tubing to transmit pressure from taps
at the foil's mid span to the top. The foil is dragged past a static cylinder using
an x-y gantry system supplied by Parker Engineering and controlled using Parker
motor controllers and proprietary motion control software. Honeywell 19CO15PG4K
pressure sensors are mounted on top of the foil, and measurements are collected at a
sampling rate of 500 Hz via a NI USB-6289 DAQ. The location of the sensor ports is
shown in Figure 4-1B.
4.1.2
Flow visualization
Particle image velocimetry (PIV) is used to visualize the flow structures associated
with measured pressure signals. PIV relies on the imaging of particles suspended
Sensor 3 Sensor 2
esr
sor
Figure 4-1: Experimental set-up. (A) picture of the experimental set-up (the foil is
moving towards the photographer). (B) schematic of the cross-section of the experiment.
in the flow field using a high speed digital camera, and illuminated using a thin
high-intensity laser sheet, as can be seen in Figure 4-2. PIV images represent a twodimensional picture of the fluid flow. Post-processing is done on the images using
correlation to create a vector field that can be used for visualization or calculation
of flow characteristics. Imaging is accomplished using a Phantom V10 high-speed
camera placed below the tank, using a 35 mm lens. The camera is capable of taking
full resolution images of four megapixels at a frequency of 500 frames per second. For
these experiments, frame rates are limited to 300 and 200 Hz and exposure times are
between 1 and 3 milliseconds.
4.1.3
Experimental parameters
The foil is dragged at velocity V = 0.5 m/s past a static cylinder of elliptical cross
section oriented at various angles. At its closest point, the foil is 5 to 10 mm away
from the cylinder. The shape parameters (as defined in Eq. 2.2) of the elliptical
cylinder are: R = 3.81 cm, [pl = 0.2. The major radius is oriented at T/4, 7r/2 or
37r/4, which corresponds to ac
- {7r/2, 7r, 37r/2}. The results from seven runs are
moving foil
stationary
cylinder
Figure 4-2: Flow visualization
discussed in the following paragraphs. The parameters for each run are summarized
in Table 4.1 (where the axis of symmetry of the foil defines y = 0).
Table 4.1: Cylinder parameters
Run
1
2
3
4
5
6
7
4.2
#
y/c
0.43
0.43
0.43
0.43
0.43
0.45
0.43
r/c
0.25
0.25
0.25
0.25
0.25
0.25
0.25
p
-0.2
-0.2
-0.2
-0.2
0.2i
0.2i
-0.2i
Pressure measurements analysis
The length of the tank allows the foil to reach a steady state before passing the
cylinder. As discussed in Section 3.1, the steady state is subtracted to the pressure
measurements in all the analysis that follows. The mean slope of the pressure is also
subtracted to the measurements to account for changes in hydrostatic pressure along
the length of the tank.
Noise characteristics
4.2.1
Typical pressure traces (the pressure traces of Run 1) are shown in Figure 4-3A. Three
distinct time periods are identified: before t = 0 s (before passing the cylinder), from
t = 0 s to t = 0.4 s (while passing the cylinder) and after t = 0.4 s (after passing
the cylinder). Before t = 0 s, the signal is dominated by noise. Figure 4-3B shows
the corresponding power spectrum. The noise is clearly not white but the spectrum
is rather messy, without any strong dominant component (the strongest component
is around 30 Hz). Between t
=
0 s and t = 0.4 s, the signal is dominated by the
interaction between the foil and the cylinder: a clear pressure peak is measured by
sensor 1, while sensors 2 and 3 measure a strong pressure drop. This time period
will be discussed in more details in the next section. The last period, like the first
one, is dominated by noise, but its characteristics are different. The noise of the last
period is dominated by a low frequency (2 Hz) component, as confirmed by the power
spectrum Figure 4-3C.
Pressure traces
A
B
15
40-sensor
Power Spectrum
t<O s
1
sensor 2
-
10
-
sensor 3
1' 20-0-
0-5-
-20
15
0
20
40
60
40
60
t>0.4 s
CoL
2 - 40 -
-60 -
_
sensor 2
sensor 3
-0.5
0
0.5
Time (s)
1
0
20
Frequency (Hz)
Figure 4-3: Pressure traces and power spectra
The main sources of noise are electrical noise from the motor and mechanical
vibrations of the foil. The high frequency components (like the 30 Hz component) are
most likely electrical noise, while low frequency components (like the 2 Hz component)
are most likely due to mechanical oscillations of the foil. Other potential sources of
noise are electrical noise from other sources and background noise of the fluid flow.
To take the noise and its variability into account, the measurement-noise covariance
R' used in the UKF is calculated for each run based on the pressure measured 0.5
to 0.3 s before the characteristic drop of pressure at the second sensor (the matrices
can be found in Appendix B).
4.2.2
Comparison between measured and simulated pressure
A close-up of the pressure measured by the sensors when passing the cylinder for
Run 1 is plotted in Figure 4-4A in solid lines (the plots for all runs can be found in
Appendix C). It is compared to the pressure predicted by the potential flow model
(dashed lines). Here again, the time period can be split into two periods: from t
=
0
s to t = 0.2 s, the measurements are noisy, but they match the predictions; for t > 0.2
s, predictions and measurements do not match any more. A vertical black dashed
line indicates the time until which measurements and predictions match. As will be
discussed in Section 5.4, the flow on the foil separates and this is why the potential
flow model stops being valid. Only pressure measurements before the black dashed
line are used to locate and identify the cylinder.
A
B
Pressure traces
60-
Pressure distribution along the foil
0
40
50
-0.05
20
0
0 (Pa)
-20- --40
-
-60
-80-
0
-- -sensor 1-5
sensor 2
- -sensor 3
-_
0.1
-0.15
0.2
Time (s)
0.3
0.4
0
0.2
0.4
Time (s)
0.6
Figure 4-4: Theoretical and measured pressure on a foil passing a cylinder.
The theoretical spatio-temporal pressure distribution along the foil is also plotted
in Figure 4-4B, showing the sensor locations (horizontal dashed lines), the position of
the cylinder center as respect to the foil (oblique dashed line), and the time at which
the model stops being valid (vertical dashed line). The figure shows that the first
sensor is located where the pressure peak is largest, while the second one, located at
maximum width, lies where the pressure drop is strongest. It can also be observed
that the flow roughly starts separating when the maximum width of the foil passes
the cylinder.
4.3
4.3.1
Object identification using pressure measurements
Process noise
In addition to noise, several sources of error affect the process of identifying a cylinder
based on pressure measurements. In the measurements themselves, an error of a few
pascal in the subtraction of the steady and hydrostatic pressure is very likely. The
pressure sensors might also have a slight drift. Modeling is the other main source
of error. Modeling errors can be geometric (errors in the shape of the foil, location
of the sensors, finite expansion for the shape of the cylinder, ...) or hydrodynamic
(mostly viscous effects). To account for all these errors, an artificial process noise is
added to the state-space representation of the problem. Since this noise is artificial, it
cannot be directly measured but has to be empirically estimated. The process-noise
covariance is chosen of the simplest form: diagonal with two degrees of freedom-one
for the size and location parameters (x/c, y/c and R/c) and the second one for the
shape parameters (p, and p.). The generic process-noise covariance is therefore:
a 0 0 0 0
0 a 0 0 0
Re=
0 0 a 0 0
0 0 0 b 0
0 0 0 0 b
(4.1)
a and b are empirically chosen such as to optimize the performance of the filter. The
values chosen for the present experiments are:
a = 4.4 x 10-6
b = 2.5 x 10-5
4.3.2
Strategy and initialization
Due to the amount of correlated noise and errors inherent to the experiments, all
attempts to fully identify the cylinder (location and geometry) in one pass have been
unsuccessful. However, fish have been observed to pass several times in front of new
objects ([33]), and it seems reasonable to assume that they first locate the objects
and estimate their size before refining their shape estimate. A similar approach is
used here: the first pass is used to get a first estimate of the position (x and y) and
size (R) of the cylinder. A second pass (using the same data) refines the first guess
and estimates the shape parameters (tx and p..).
For all experiments, the UKF starts as the pressure stops being statistically zero
and is initialized with 100% error. The covariance matrix is empirically initialized to:
0.4 0
Pxo= [0
0
0
0.4
0
0
0.4
(4.2)
After the first pass, the final location and size estimates are used to initialize the
UKF for the second pass, and the shape parameters are initialized to zero (a circle).
The covariance matrix of the second pass is initialized as a block diagonal matrix.
The first block is the final covariance matrix of the first pass augmented by 4 x
10-3 on the diagonal (to account for the fact that the best estimate under circular
assumption might not be the same as under elliptical assumption) and the second
block is (084
0.04).
The UKF starts slightly later for the second pass than for the first
pass so as to emphasize the data that have the lowest noise/signal ratio.
4.3.3
An example of object identification
The process of cylinder size and location estimation as described above is shown in
Figure 4-5 for Run 6. The evolution of the three parameters is plotted in solid lines.
They all stay above their theoretical value (dashed lines) during most of the run, but
end up converging to their theoretical value. Configurations corresponding to four
times indicated by letters a to d are also sketched. The dashed blue ellipse shows the
actual position and shape of the cylinder while the red circle shows the UKF estimate
of the position and size of the cylinder at the corresponding time.
Size and position estimation
---
4--
a
I'I
0
a
b
c
d
------
-------
-0.5
x/c
b
c
d
0.05
0.1
Time (s)
0.15
<~><
~
0.2
Figure 4-5: Experimental object localization
Figure 4-6 shows the evolution of all parameters during the second pass. The
value of the location and size parameters, identified during the first pass, do not
significantly change during the second pass. The shape parameters immediately jump
to their actual value and then slightly oscillate around this value.
0.6
Shape identification
12
a
b
C
d
0.4
0.2
0
C
a)
0
E -0.2
0.1
Time (s)
Figure 4-6: Experimental object identification
Figure 4-7 shows the measured (solid lines), filtered by UKF (dashed lines) and
predicted by theory (dotted lines) pressure for the first (Figure 4-7A) and second
pass (Figure 4-7B). As can be seen, the measurements are very noisy, especially at
sensor 3, but the filtered pressure is very close to the predicted pressure, especially
during the second run. It appears clearly that as the filtered pressure gets closer to
the predicted pressure, the estimated shape gets closer to the actual shape of the
cylinder. This run is the perfect example of the first pass being used to get a rough
estimate of the size and location of the cylinder, and the second pass building on the
estimates of the first one to get a more precise estimate of the object shape.
A
40,
40
20
20-
0
0
B
R,
CA
-20
40
0
-
sensor 1
-
-sensor2
sensor3
-20 - -
sensor1
-sensor2
sensor 3
0.05
0.1
Time (s)
0.15
0.2
-40
0
0.05
0.1
0.15
0.2
Time (s)
Figure 4-7: Measured (solid lines), filtered by UKF (dashed lines) and predicted by
theory (dotted lines) pressure for the first (A) and second (B) pass.
4.3.4
Performance of experimental object detection and identification
The plots showing the evolution of the estimated parameters as well as the measured,
filtered and predicted pressure traces for all runs can be found in Appendix D. It can
be seen that all object localizations are quite accurate. It is interesting to notice that
the estimated circle best fits the part of the ellipse that is closest to the foil. Similarly,
even when the global shape of the ellipse is not very accurately identified (like in Run
4), the estimated ellipse fits very well the bottom part of the cylinder. Run 5 and
7 are also interesting. For these runs, despite the fact that the size is not very well
estimated, the shape estimate is surprisingly accurate. The object size and shape are
encoded separately and, to some extent, they can be estimated independently.
We will now look more globally at the performance of experimental object identification and compare it to the performance predicted by our analysis in 3.4.1. The
results of experimental object identification are summarized in Table 4.2. For each
run, Table 4.2 displays:
0 o- =
/|
Rc ||2
* p = y/T,
* r=
the actual vertical position of the cylinder center
r/T, the actual mean radius of the cylinder
p, the actual shape parameter of the ellipse
p
Sd= d/T
=
- fI1 -
|-
0.5, the minimum distance between the foil and the
cylinder
* A
Q the error percentage in final estimate of the vertical position of the cylin-
der center
" Af/f, the error percentage in final estimate of radius of the cylinder
* Ad/d, the error percentage in final estimate of the minimum distance between
the foil and the cylinder
Using the analysis developed in Section 3.4.1, with Apo
=
10 Pa, we expect distance
and radius errors on the order of 0.4d, which is very close to observed errors.
Finally, it is interesting to notice that the distance to the cylinder is the parameter
that is best estimated, which stands even more clearly if absolute errors are considered
instead of percentages. This indicates that the distance to the cylinder might be a
more relevant parameter than the object center location. We also observed that the
portion of the ellipse that is closest to the foil is usually best estimated. These two
observations suggest that a local surface parameterization might be more appropriate
to the use of pressure sensors than our global shape parameterization.
Moreover,
Table 4.2: Results of experimental object identification
Run #
1
2
3
4
5
6
7
o6
8
8
9
7
7
8
2.4
2.4
2.4
2.4
2.4
2.5
2.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
A
p.
-0.2
-0.2
-0.2
-0.2
0.2i
0.2i
-0.2i
d
0.2
0.2
0.2
0.2
0.5
0.6
0.5
Aq/P
0.2
0.2
0.003
0.2
0.3
0.2
0.3
Af/f
0.2
0.1
0.2
0.1
0.3
0.3
0.5
Ad/d
0.1
0.1
0.1
0.1
0.4
0.2
0.1
lAp|
0.3
0.3
0.2
0.1
0.1
0.1
0.1
in the perspective of underwater vehicle navigation, a local characterization that
could apply to any obstacle would also be more appropriate than a global shape
identification.
72
Chapter 5
Discussion and further simulations
5.1
Sensing range
Hydrodynamic imaging is known to be a short-range sense (1361), and in the experiments discussed in the previous chapter, the foil passes less than 0.1 body length
from the object. How far away can an object be detected (depending on its size), and
is there a way to increase this distance?
The first half of the question has been investigated in Section 3.4.1 based on the
amplitude of the pressure signal. We will now look at the actual performance of
the algorithm using simulated pressure data. The pressure is simulated using the
algorithm described in Section 2.3, and a white Gaussian noise of variance 20 Pa 2 is
added to simulate noise of magnitude comparable to experimentally observed noise
(see Appendix B). The other parameters used in the simulations are set to the values
identified for the experiments (Section 4.3.1 and 4.3.2) and the strategy described in
Section 4.3.2 is used to identify the object. The cylinder used in the simulations has
shape parameters r = T, p, = -0.2 and p. = 0.1 and the speed of the foil is set to
V = 0.5 m/s.
Using these parameters and strategy, it is found that the detection range is about
d = T. A localization and identification process is shown in Figure 5-1A&B for such
a distance. At that distance, it takes a while before the foil notices the presence of
the object, but once it detects it (t ~_0.1 s), the position and size parameters con-
vergence is very fast. Figure 5-1C&D show the corresponding simulated (solid lines)
and filtered by UKF (dashed lines) pressure traces.
Size and position estimation
A
Shape identification
B
me (s)
Time (s)
5b
a
00
002
002
004
002
0
-01
-0.0
ON
01c
_
0
-0.15
-01
-005
-01
005
0
1008
008
K
0.04
0
9-0.0600
0
0..2
004
004
002
002
0
-005
0
P000000)
005
0
000
01
-005
0
005
Posb
0
(M
00
1
posbn(M)
Pressure
-20'
0
'
0.1
''
. 'I
0.2
Time (s)
0.3
0.4
0
0.1
0.2
Time (s)
0.3
0.4
Figure 5-1: Identification of an ellipse located at maximum sensing distance.
The pressure signal amplitude at that distance is around 8 Pa, i.e. between once and
twice the standard deviation of the noise. Table 5.1 summarizes the object identification performance in this simulation. It displays the (final) estimates and their
respective error, as well as the corresponding Apo based on the analysis of Section
3.4.1. The values found for Apo are about one order of magnitude smaller than the
noise standard deviation. These results show that our UKF is very good at filtering white Gaussian noise. In the presence of white Gaussian noise, our algorithm
can achieve estimates much more accurate than would be expected from the value of
the standard deviation. However, the distance at which it can detect objects is still
dictated by the noise standard deviation. It seems that the main limitation of the
algorithm is its sensing range.
Table 5.1: Object identification performance using simulated data
Parameter
Value
Error
Apo
f
1
0.1
2
2.8
0.2
X
d
1
0.05
1
t
-0.2 + 0.li
0.07
0.5
In all the cases considered so far, the flow is generated by the moving foil. However, as discussed in Section 3.1, the presence of an outside flow can considerably
increase the amplitude of the pressure signal, thus allowing objects to be detected
further away. The same simulation as described above has been run with the addition
of an outside flow of velocity U = 0.1 m/s oriented against the motion of the foil. It is
found that the object can be detected as far as d = 2.5T away from the foil. This is a
considerable improvement (as compared to d = T in static water), for the addition of
a relatively slow outside flow. The convergence of the location and shape parameters
at that distance is shown in Figure 5-2A&B. The corresponding measured and filtered
pressure (respectively solid and dashed lines) are shown in Figures 5-2C&D. Like in
the absence of outside flow, the amplitude of the pressure signal is comprised between
once and twice the standard deviation of the noise.
In reality, the presence of outside flow might increase the ambient noise, which is
not taken into account here, but it clearly has the potential to increase the detection
range.
Size and position estimation
A
Shape identification
B
S0.8
E
1to
0.6
2
0.4-
Q.
.
C
-0.2------
-
0
-0.2'
L
0.2
Time (s)
'
0.1
0
0a
0.4
0.3
001-
0
0.1
0.3
0.2
ime (s)
a
010
b
0
010
0
b-
10.0
005
?
0
-0.05
-015
-0.1 -000
0
0.05
0.1
0,15
01
-015
-01
-005
0
-015
005
015 dd
0.15
0.05
00
10
-0.1
-005
0
005
C
20
C
0
0.05
Pos4ion
{M)
01
0
-000
0.1
005
-5 d
0.05
00n
0
005
-010
d
1000
-01
0
-0.05
0
0.05
01
Posirn (m)
0.15
0
0,05
-0.1
0
0.05
-005
01
Fressure
0.1
0.15
Ptoknm
Pressure
D
In
0.05
0
Posibon(M)
10
10
0.
a-
0
0
C)
(L
|'
0.2
Time (s)
"oI
0.4
1
,
0.1
0.2
-
0.3
sensor 1
sensor 2
sensor 3
0.4
Time (s)
Figure 5-2: Identification of an ellipse located at maximum sensing distance with
outside flow.
5.2
Impact of sensor density on object identification
Another limitation of the algorithm performance using experimental measurements
is the very limited number of pressure sensors used. Due to the available sensor size,
only three pressure sensors have been used in the experiments described in Chapter
4. With three sensors, an error or drift of a few pascals on any sensor can seriously
impair the performance of object detection and identification.
To illustrate this phenomenon, the same simulation as the one described in Section 5.1 (without external flow) has been run, simulating a drifting sensor. A linear
drift reaching 10 Pa at t = 0.3 s has been added to sensor 2 to simulate a drifting
sensor (so it is a drift of 33 Pa/s). The drift does not significantly impair the ability
to detect the presence of the object, but it strongly affects the global performance
of object localization and identification. As can be seen in Figure 5-3A, when the
object is detected (shortly before t = 0.1 s), the estimates quickly jump to values
close to their actual value, but then drift away (unlike in Figure 5-1A). The second
pass (Figure 5-3B) does not improve the size and location estimate and the final
estimated shape is very different from the actual shape. Figures 5-3C&D show the
corresponding pressure traces.
Having more pressure sensors would make the algorithm performance less sensitive to the presence of a faulty sensor. The simulations with and without the faulty
sensor have been run with a denser array of pressure sensors (20 sensors equally distributed on the front two third on both sides of the foil). As can be seen in Figure
5-4A, increasing the sensor density does not increase the distance at which objects can
be detected, but it significantly increases the convergence speed of the parameters.
Figure 5-4 shows the results of object detection and identification using the denser
array of pressure sensors.
When one of the sensors is faulty, the advantage of having a denser array of pressure sensors is more significant. Figure 5-5 shows the results of object detection and
identification with an array of 20 pressure sensors, with the one located at maximum
width on the side of the object having a linear drift. As expected, the drift of one
Size and position estimation
A
0
0.1
0.2
Time (s)
0.3
0.4
Ti me (s)
0.2
0.12
0.1
0
-0.02
-0.05
-0.15 -0.1
-0.05
0
0.05
Posiion(m)
01
C
0.25
0.15
-0.1
01
-0.05
0
0,05
POSRMM
(M)
-0 1
-0.05
0
0.05
0.15
C
0-15
0.04
0
0.1
Posioon(m)
0.2
0.05
0.1
d
05
01
-01
0
0
005
0.02
0.05
-005
01
'90.06
0.1
-01
PoL40in
(m)
01
E0.15
01
-0 15
0.15
0.08
02
b
005
015
0.05O
Shape identification
B
0
005
Posion (m)
-0.1
01
-0.05
0
0.05 0
Posibon(M)
1
0
0.15
0
-0.05
0
0,05
0.1
POSAge
(M)
0.1S
Pressure
C
20
10
a.
-
-10
sensor 1j
-
sensor 2
-20
0
0.1
0.2
Time (s)
sensor 3
0.3
0.4
-20'0
0.1
0.2
Time (s)
0.3
0.4
Figure 5-3: Identification of an ellipse located at maximum sensing distance, with a
drifting sensor
Size and position estimation
A
-0.2'0
0.1
0.2
Time (s)
Shape identification
B
0.4
0.3
Time (s)
0.1
..:
£008
004
00
SIa
1
0'
'
0.08
,
00D4
I00
002
-0.1
01
-0.05
PostiOn(M)
0
0.05
Posilon(m)
0.1
b
£0
0.02
-015
-01
-0.05
Position
(m)
0
-01
-0.05
Posiion(m)
0
0.05
Position
(m)
0
7
£008
002
-005
0
005
Position(mn)
0
-0,05
0
Posiion(i)
005
OI
Figure 5-4: Identification of an ellipse located at maximum sensing distance, with a
denser array of pressure sensors
Size and position estimation
A
Shape identification
B
0.6 a
(
d
X/
0.4
--
E
L
"o. 0.2x-
R/c
-pX
0
0
0
0.2
Time (s)
0.1
0.'
0.3
-0.4
0
0.1
0.2
0.3
0.1
Time (s)
o,a
oos-,
0.08
0.08
005
006
,
0,04
008
10040
00
002
0.02
0.02
-005
-- -- --
--
- - --
-0.2-
01
-002
-0.15 -01
-0.05
0
0.05 0.1
Posdbon
()Posldon
0.15
-01
01
-000
00
0
0
0.00
0.0
(m)
0
-015
0
-005
-0.1
Position(M)
-01
-005
Position(m)
0
d
000 C
0 06
0
0
O0
0.04
002
0.02
0
0
-005
0
Posiion(M)
0.05
0
005
Positon(M)
01
-0.05
0
Position(M)
0.05
0
0.05
0.1
Positon(m)
Figure 5-5: Identification of an ellipse located at maximum sensing distance, with a
drifting sensor in a denser array of pressure sensors
sensor goes unnoticed in the presence of a dense array of pressure sensors.
More interestingly, a dense array of pressure sensors is also more robust to a given
probability of failure of the pressure sensors. For example, consider sensors that have
a probability 1/3 of drifting. Assume the slope of the drifting sensors is given by a
normal distribution of mean 0 and standard deviation 33.33 Pa/s. Figure 5-3 illustrates this case with 3 sensors (except that the drift is not randomly chosen) and
Figure 5-6 illustrates it with 20 sensors, one every three sensors drifting. Comparing
Figures 5-3 and 5-6 shows that increasing the number of sensors improves the convergence of the object identification algorithm and the accuracy of the final estimate.
A
Size and position estimation
-I---
Shape identification
B
X/C
y c
a7
a
-A
'
5
0
b
c
d
0.1
0.2
Time (s)
0.3
01
0.08
0.05
0.06
0
0..
a
-0.5
0
bCd
0.1
0.2
Time (s)
0.3
0.
b
0.08
0.06
004
-
0 02
0
0.04
0.02
0
-005
-015
-01
0.05
-0.05
0
Postion(m)
01
0.1
-01
015
-005
Position(m)
0
0.05
m)
0
0.1
0.
0.08
00
a006
EOOO
0.04
004
0.02
0.02
0
0
-005
0
Position(m)
0.05
-0.1
-0,05
Position
(m)
0
0,05
Position(m)
0.1
-
0.02
01
0
0,05
Position
(m)
0.1
81)
005
0
Figure 5-6: Identification of an ellipse located at maximum sensing distance, with
1/3 of the pressure sensors drifting
A dense array of pressure sensors is therefore more robust to a probability of some
sensors being defective, but there is also another reason why you might want to use a
dense array of pressure sensors. One way to estimate the appropriate sensor density
is to simply look at the pressure gradient along the foil passing an object, as done in
Section 3.4.2. An alternative approach is to examine the effect of sensor density on
object identification performance.
It has been observed in Section 3.1, that in the active sensing scheme, sampling
frequency and sensor density are not equivalent, due to the fact that the pressure
signal along the foil does not simply translate in time. Therefore, there might be
an optimal sensor density below which the lack of spatial density cannot be compensated by a higher sampling frequency. The optimal density might very well depend on the size and distance of the cylinder, but by way of example, the case of
the foil passing at d
cm and y
=
=
0.3T from a cylinder with geometry parameters R = 1.5
0.2i is investigated here. White Gaussian noise of standard deviation
2 Pa is added to the simulated pressure measurements. Between 10 and 70 pressure measurement points are evenly distributed along the front two thirds of the
foil (as illustrated in Figure 5-7C) and the sampling rate (f) is chosen as the ratio
f = 20000/(number of sensors) (such that the average frequency is 500 Hz). The
final error is calculated as E = I (
+ +
A+
p2 + Ayt), where A(-) is the
difference between the final estimate an the actual value of parameter (.). For each
simulation, the convergence time (time elapsed before E < 0.2) and the final error is
calculated. Each case is simulated twelve times and the time of convergence and final
error mean and standard deviation are plotted (Figure 5-7A&B). Both convergence
time and final error plots suggest that, at least for the configuration considered here,
when the sensor spacing is greater than 5 mm, the performance of the object identification decreases. Amazingly, the optimal spacing suggested by these observations
scales with the actual spacing of lateral line canal neuromasts in the trunk canal of
blind Mexican cave fish that can be estimated from Figure 1-1A (roughly 1 mm for
a 6 cm long fish).
5.3
Pressure sensors or pressure gradient sensors?
The work presented in this thesis is based on pressure measurements. However, canal
neuromasts of fish are known to respond to pressure gradients ([7]). Would there be
A
Convergence Time
Figure 5-7: Convergence time (A) and final error (B) of the object identification as a
function of sensor spacing. (C) shows the sensor locations for a spacing of 6 mm.
any advantage in using pressure gradient sensors instead of pressure sensors? As we
shall see, probably...
When moving in open water, a fish creates a pressure field that it can recognize
as being its own. In the case of a simple forward motion, this pressure field is characterized by a high pressure at the front, and low pressure along the main part of
the body (Figure 3-4A). When gliding past an object, the pressure change induced
by the presence of the object can be quite small compared to the ambient pressure
field, which is why, in this study, the steady pressure field has been subtracted to
every pressure trace. However, as can be seen in Figure 5-8A, the ambient pressure
gradient along the body is pretty small. So measuring the pressure gradient (as fish
do) reduces the ratio signal of interest over total pressure (except at the very front of
the foil). As was mentioned in the introductory chapter of the thesis, this is one of
the advantages of the lateral line canal subsystem over the superficial subsystem.
Moreover, using pressure gradient instead of gradient would annihilate the need
to take into account the hydrostatic pressure and subtract the steady pressure. Since
both have been identified as potential sources of errors, getting rid of them should
improve the performance of the algorithm.
Figure 3-4A also suggests distinct uses of the head and trunk canals. As investigated by Windsor [371, when approaching a wall head-on, the increase in pressure
gradient is confined to the head. Figure 3-4A shows that, when gliding past an object,
Total pressure gradient
A
B Unsteady pressure gradient
0
0
3000
2000
0.05
-0.05
0
1000
0
0
0 (Pa/m)
0.1A
-0.1
- 0.
1
-1000
-0.15
2000
-2000
-0.15
0
0.2
0.4
Time (s)
0.6
0
0.2
0.4
Time (s)
0.6
Figure 5-8: Pressure gradient signature
no noticeable change in pressure gradient happens along the head. Therefore, head
canal neuromasts are probably mostly used for obstacle avoidance while the trunk
ones serve for object identification.
5.4
Limits of the potential flow model
The results from Section 4.3 demonstrate that object localization and recognition are
possible with experimental pressure measurements. However, only the pressure measured before the maximum width of the foil passes the cylinder are compatible with
our model. Indeed, as has been observed in Section 4.2.2, the potential flow model
stops being valid after this point. Flow visualization has been used to investigate
the transition that causes the potential flow model to stop being valid (the set-up is
described in Section 4.1).
Figure 5-9 compares the velocity field predicted by the inviscid model to the experimental velocity field measured using Particle image velocimetry. As can be seen,
both flows are quasi-identical everywhere, except in a small region materialized by
green and orange ellipses. To get finer details of the flow characteristics in the small
region of interest, an individual particle has been followed, and its pathline is marked
in green in Figure 5-10. It appears very clearly in the frame sequence that between
t = 0 s and t = 0.1 s the particle is in a laminar flow, but between t = 0.1 s and
Simulated Flow Velocity
B
Particle Image Velocimetry
Figure 5-9: Comparison between experimental and simulated velocity field
t = 0.2 s, the flow separates, as the particle starts swirling. Separation affects the
entire pressure field around the foil.
U
Figure 5-10: Flow separation: a pathline
Figure 5-11 shows the pressure gradient distribution along the foil as it passes
the cylinder for the configuration of Runs 1 to 4. The pressure sensor locations are
represented by horizontal dashed lines, an oblique line marks the position of the cylinder and a vertical line marks the approximate time when the potential flow model
stops being valid. This line also coincides with the onset of a strong adverse pressure
gradient (orange patch in the middle of the figure), which theoretically explains why
the flow separates.
Viscous effects were already known to strongly affect the signal measured by surface neuromasts as well as the dynamics of the flow in the canals ([35]).
However,
in the cases previously studied (vibrating sphere), viscous effects did not affect the
pressure gradient measured by canal neuromasts (129]). We show here that in the case
Pressure gradient along the foil
0
5000
0.05
0
(Pa/m)
-0.1
-5000
-0.15
0
0.2
0.4
Time (s)
0.6
Figure 5-11: Unsteady pressure gradient along thee foil
of a fish gliding past an object, viscous effects strongly influence the signal measured
by canal neuromasts.
Chapter 6
Conclusions
The blind Mexican cave fish, able to dart in the dark and identify the shape of static
objects in static water by gliding past them, has been used as an inspiration for a
novel object identification algorithm based on pressure sensors. A two-dimensional
potential flow approach based on a source panels method has been used to characterize the pressure distribution on a vehicle passing a static object in stationary
flow. A shape parameterization inspired from conformal mapping was applied to independently encode the position, size and shape of the object. Finally, the unscented
Kalman filter has been adapted to take into account the fact that two bodies cannot
physically intersect.
Experiments have been run in a tank, using an instrumented foil moving past a
cylinder, to test the method developed. The algorithm has proved to be very successful at locating the cylinder, and mostly successful at identifying it, despite a strongly
correlated noise. It has been observed that since the location and size are encoded
separately, the shape of the cylinder can be identified even when the size and location
estimates are slightly offset.
Based on simulations using a NACA 0018 foil to model the fish, the distance at
which an object can be detected (depending on its size) has been estimated. It has
been found that for the amount of noise experienced in the laboratory, the sensing
range is about the width of the foil. However, simulations have shown that the sensing range can be significantly increased in the presence of an outside flow.
The experiments performed used three commercial pressure sensors and it has
been shown that increasing the number of pressure sensors should make object detection and identification more efficient and more robust to sensor failures. Estimates
based on typical pressure gradient values and object identification performances, independently suggested that a spacing of 5 mm between pressure sensors was optimal.
These estimates justify the need in micro mechanical pressure sensors for efficient
object identification.
In this study, the steady pressure has been subtracted from every measured and
simulated pressure to make the pressure generated by the cylinder more noticeable.
This need can however be eliminated by measuring pressure gradient, as fish actually do. We have also observed that while the front 10% of the fish (or foil) is key
to obstacle avoidance, measurements along the following 50% are essential to object
identification.
Finally, we have shown that the potential flow model gives accurate predictions
of the pressure field, until the flow separates.
Chapter 7
Recommendations for future work
On the experimental side, running experiments described in Chapter 3 with a denser
array of pressure sensors (ideally a dense array of micro pressure sensors, when those
become available), would allow a better comparison between the pressure field predicted by our potential flow model and the measured pressure.
Simulating the interactions between the moving foil and the stationary object in
viscous flow would also help identify the impact of viscosity on the pressure measured along the foil. A learning algorithm could then be used to develop an efficient
(on-line) algorithm that uses both potential flow and viscous features of the flow to
identify objects.
The unscented Kalman filter has been observed to be more efficient at object identification than at object detection. In the case of an underwater vehicle navigating
in an unknown environment, it would be advantageous to use an efficient detection
algorithm and limit the use of the unscented Kalman filter to object identification.
Finally, investigating object identification has brought insight into parameters
that affect the pressure along a body exploring its environment. We have observed
that the distance of the object is a more relevant parameter than its center position.
We have also observed that the pressure along the foil is much more sensitive to the
nearby portion of the object than to its global shape. Moreover, when navigating
underwater, knowing the shape and position of the closest boundaries and obstacles
is probably more useful than knowing the actual shape of relatively small objects.
Therefore, a more local shape or boundary parameterization should be considered in
the future.
Appendix A
Alternative definition of sensitivity
In this Appendix you will find the same figures as in Section 3.3 with the sensitivity
defined as the integral over the length of the foil and over time of |dp/dx|.
A
20*1og(Jjdp/dal di dt)
B
Linear regression
0
0.5
0.5
-20
0
0
-40
-60
-0.5
-0.5
-80
-1
--
-0.5
0
Iog(d/T)
0.5
1
100
-0.5
0
log(d/T)
Figure A-1: Sensitivity to distance
0.5
1(dB re 1Pa 1m 1s)
0
-0.5
1
log(d/T)
0.5
Figure A-2: Sensitivity to distance for fixed sizes
-50 L
-1I
0.5
0
log(d/T)
-0.5
0
log(d/T)
1
Figure A-3: Sensitivity to size
A
20*Iog(fdp/djp|| di dt)
0.9
0
0.8
-10
0.7
-20
0.6
-30
0.5
0.4
-40
0.3
-50
0.2
-60
0.1
-0.5
0
log(d/T)
0.5
-70
1 (dB re
1Pa 1m 1s)
:1
-0.5
0
log(d/T)
0.5
Figure A-4: Sensitivity to eccentricity for a horizontal ellipse
92
A
20*log(fjdp/d5 dl dt)
0
0
oa=nT
a=0.7
*,
-0.5
0
log(d/T)
-10
-10
-20
-20
-30
-30
-40
-40
-50
-50
-60
-60
-70
(dB re
1Pa 1m 1s)
0.5
1
*
*
y=-1 5x-21
y=-56x-9
-7n
-0.5
1
0
log(d/T)
Figure A-5: Sensitivity to orientation
0
---ellipse
triangle
-square
-20
-40
-60
-80
-100
-1
-0.5
0
0.5
log(d/T)
1
Figure A-6: Sensitivity to shape
1.5
0.5
1
94
Appendix B
Measurement-covariance matrices
Measurement-covariance matrices (in Pa 2 ) for experiments (Chapter 4) and simulations (Chapter 5) are gathered in this appendix.
Run 1
K
K
13
R%
Run 2
RC~
3
3
32 12
3
12
21
7 6
(B.1)
16
42 14
6
14 27
27
4
(B.2)
Run 3
C=4 4
Rc
5
45 21
5
21
29
28
9
7
60
24
(B.3)
Run 4
7
24 22
(B.4)
1
Run5
Rc =
29
9
9
9
14
11
9
11 22
(B.5)
Run 6
22 10 13
Rc
10
14
16
(B.6)
13 16 35
Run 7
26 14 18
Rc
14 15 18
(B.7)
18 18 36
Simulations
20 0 0
Rc
0
20
0
0 0 20
(B.8)
Appendix C
Pressure measurements figures
In this appendix, the pressure traces from the experiments (solid lines) and the pressure traces predicted from the potential flow model (dashed lines) are displayed.
-20-
-40-60-800
0.1
0.2
Time (s)
0.3
0.4
Figure C-1: Pressure measurements, Run 1
-100'L
0
0.1
0.2
Time (s)
0.3
0.4
Figure C-2: Pressure measurements, Run 2
0
0.1
0.2
Time (s)
0.3
0.4
Figure C-3: Pressure measurements, Run 3
50-
C-
0,
-
-
a- -50o
---100
0
sensor 1
sensor 2
sensor 3
0.1
0.2
Time (s)
0.3
0.4
Figure C-4: Pressure measurements, Run 4
-50'0
0.1
0.2
Time (s)
0.3
0.4
Figure C-5: Pressure measurements, Run 5
0.1
0
0.2
Time (s)
0.3
0.4
Figure C-6: Pressure measurements, Run 6
40
20-
-20-
1 '
-40-sensor
-0--sensor 2
-
-60
0
'
sensor 3
0.1
0.2
Time (s)
0.3
0.4
Figure C-7: Pressure measurements, Run 7
100
Appendix D
Experimental object identification
figures
This appendix shows the the convergence of the estimated parameters for experimental object localization (on the left) and identification (on the right). It also compares
the shape of the estimated object (in red) to the actual object (dotted blue ellipse) for
several times. It finally shows as the measured (solid lines), filtered by UKF (dashed
lines) and theoretical (dotted lines) pressure traces.
101
Shape identification
0.
---R/c
x
0. 2
-0.5'
0.05
0
0.1
0.15
-0 .2
a
-n
a
0.
0
4
bcd
Time (s)
a
0.2
0.15
0.1
0.05
Time (s)
b
o
0.15
0.12
a
0.1
001
005
b
.-
008
0080
0.06
006
004
o0 04
0.02
002
0
-000
-00
-02
-015
-01
-0.06
Posdion(M)
-02
0
- - - -- ---- - --0.15
02-002
---
C
0
-0.1
0.1
-0.2
-0.10
Position(m)
0,12
onid
0.12
00
0.08
-015
0
C
0 d
0.08
0.061
006
00
004
C
0.00
0
0.02
002
0
-010 -0 1 -0.05
0
Pboeon(m)
0,05
-0.15
01
-0.1
-0.05
Positon(m)
-0.15
0
0.05
0.1
-0.05
-01
Posib (M)
"
-0.15
0
Pressure
>ressure
-100 L
0
-0.02,-
-0.02
0
0.15
0.1
Time (s)
Time (s)
Figure D-1: Object identification, Run 1
102
0
-0,05
-0.1
POSOn(m)
012
01
006
-0 05
-0.1
PoiM (M)
-.005
-0.1
Postion(m)
0
Size and position estimation
Shape identification
0.6 La
a
0.4
2
0.2
0
E
c0
$a) 0.
C
E -0.2[
-0.4 -
0
0.1
Ti me (s)
0.05
a
0.15
0.2
Time (s)
0-12
008
0.05
006
0,02
0.02
-002
015
01 -0.05
Position(m)
0.04
-00-
0
-0.2
-015
-0 1
-005
0
012
-0 1
-0.05
Poston(M)
-015
0
008
0.06
006
0,04
0.04
0.04
002
0.02
0.02
00
-0.1
Poston()
-005
0
0.12
0.08
01
-0.15
012
01 d
C
-0.0
-02
Poiton (m)
c1
0108
012
0.08
0.04
"0
0.2
006
006
0104
0
-000
a-
0.1
0.08
00
0.1d
0.08
-
006
004
002
0
0
-02
-0.15
_.1
-0.05
Positin (m)
0
0.05
-015
-0.1
Poton (m)
-0.05
0
-015
-0.1
-0.05
Psftloo(m)
0
-0.15
-01
-005
PosOoo(M)
Pressure
essure
100
50
0
-
-50
1inn
0
0.05
0.1
Time (s)
0.15
0
sensor 1
sensor 2
sensor 3
0.05
0.1
Time (s)
Figure D-2: Object identification, Run 2
103
0.15
0
Shape identification
Size and position estimation
0.6
0.4
0.2
0
-0.2
-0.4
0.1
0.05
0
Time (s)
0.12
0,a
0.15
b
0.08
0.0
0.04
0.02
01
-0
-0.2
-0.15
-015
0
-01
-0 05
Posiom(M)
-0.1
-005
0
012
012
0.1 C
008
-
0.08
0,04
0.04
0.02
0.02
Posinon(m)
0
-0.021
-0.02
-015
-0.1
-0.05
-0.15
0
poside (M)
Pressure
0.1
Time (s)
Figure D-3: Object identification, Run 3
104
-0.05
-01
(m)
P08.808
0
Size and position estimation
Shape identification
0.1
Time (s)
Time (s)
o, b
012
012
0.04
0.08
0.00
K .
004
002
-0 15
-0.1
-0.05
0
-0.2
Position(m)
-015
-0.1
-005
Poson Iml
0
-0.02
-02
-015
-0.1
poho
(
I
-0.05
-0.15
0
012
0.12
0.08
00M
D.06
0.04
0.02
0,06
0.06
0 04
004
0.04
002
0.02
0.02
012
0.1 d
0.1
0
-
0 02
-002
-0.02
-02
0 04
0
0.04
-
0.02
0
0.06
-0.1
-005
0
012
C
0Ad
0 08
0,08
0
-0.0
-02
-0.15
-0.1
-0.05
Posin (m)
0
-0.15
-0.1
-0.05
Posn (m)
-0,15
0
-01
-0.05
Postio (m)
-0.15
0
Pressure
Pressure
0.1
0.1
Time (s)
Time (s)
Figure D-4: Object identification, Run 4
105
-0.1
-0.05
PosMon(m)
0
Shape identification
Size and position estimation
0
0.1
Time (s)
0.05
0
0.
0.15
1 b-
0
0,1
0.08
0.08
00.02
0
0.04
002
0
-0.02
-0.2
-015 -0.1 -0-05
Posiion(m)
0.2
002
0.,a
0.12
01a
0.15
.
Tim e (s)
0.05
0
-0.2
012
0.1 C
-002
0-015
-0.1
-005
Position(m)
-0.2
0
-0.15
0
-0.05
-0.1
old
01C
0.082
0.08
0.06
-0 .15 -01
0
:
0.04
0.04
0.02
0 02
0.02
0
0.
d
006
Z006
0.08
0.04
-000
Posion(m)
Position(my
0.02
0
-002
-0.15
-0-.
-00I
-0.1
-0.05
Position
(m)
0
-0 15
-01
-0,05
Poston
(M)
-0.1
P.d
-0.15
0
-0.05
(m)
0
-0.15
-01
-0.05
Psin(m)
Pressure
Pressure
60
40
20
I
0
-20-
-40
0
0.05
0.1
Time (s)
0.15
0
---
sensor 1
-
sensor 2
sensor 3
-
0.05
Figure D-5: Object identification, Run 5
106
0.1
Time (s)
0.15
0
Size and position estimation
Shape identification
0.6
(
-
0.4
E
. 0.20
0
C
E -0.2-0.4
Time (s)
a
-
0
0.05
0.1
Time (s)
012b
a
01
0.15
0A
002
0.00
01
004
-002
0
01
-0.2
-0.15
-0.1
-0.05
Postfion(m)
0
-02
d
0.12
0.1
012
-015
c
0
-015
-
0.1
0.08
02
0.1
000
006
0.02
"
d
0 02
0
-002
-0.15
-01
-0.05
0
Fressure
40
20
a.
0-
O-
0.05
0.1
Time (s)
0
-0-02
-015
P05ii (M)
Posilon (m)
Pressure
0
-
004
002
-0.02
0.1
Time (s)
0.15
Figure D-6: Object identification, Run 6
107
0
0.06
S0-04
0.04
-01
-0.05
Posit"On
(M)
0.08
0,06
0,06
Postion (m)
-0.1
-005
Posioon(m)
-0.1
-005
PosiUn
(m)
0
0 05
S0.4
D
-
--
/c
-
r.-- - -- -
0.22
C/
CD
a
0
c
0
--
-0.2L
aJ
0.05
0.1
Time (s)
C
-0.4
0.2
0.15
0
0.05
Time (s)
015
0501
-E0
b
0.15
015
00-.
-
01
0 05
-
005
010
-
01
-0
0
?01
02
000
-0.2
-015
-0.1
-0 05
-02
0
-0.15
Position(M)
15 c
-01
-005
Position(M)
0
d
0.1
0.1
0.05
0.5
0
0
01
-015
-01
-005
Posin (m)
0
05 5
-015
-01
-0.05
Posin (m))
0
-015
0.0
-0.1
-0.00
0
0.05
-0.15
Position(m)
-0.1
-005
Position(m
Pressure
Pressure
60
40
20
0-
-20
-40
0
0.05
0.1
Time (s)
-60''
0
0.15
-
sensor I
-
,Anqnr 2
0.05
0.1
Time (s)
Figure D-7: Object identification, Run 7
108
0.15
0
0.05
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